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Loan Calculation

You are considering taking out an $800,000 30-year loan with equal monthly payments with a bank, which quotes annual rates on its deposits and loans of 1.2% and 3.6%, respectively.

  • Without constructing a loan amortizationschedule,
  • calculate the amount of interest that will be paid in the first month of the 25th year into the
  • calculate the total amount of interest that will be paid over the life of the
  • Interpret your answer for (a)(ii) and discuss the limitation(s), if any, of such an interpretation.
  • Calculate the present value of the loan payments using a discount rate of2%.
  • Interpret your answer for (c) as well as the difference between that answer and the actual loan principal. What can explain thisdifference?
  1. Holdings, an Asia-Pacific telecommunications company, has excess capital and is looking to make a regional telecommunications investment. S. Corp won the contract to advise T. Holdings on the potential of the investment, and allows T. Holdings to pay for its charges in annual installments, starting at $2 million for the next year, and increasing at 10% annually until the final installment in the fifth year.

The project under consideration entails an initial infrastructural investment of $600 million, and subsequent investments of the same amount every five years. These assets will be depreciated on a straight-line basis to a book value of zero five years from the purchase, but can be salvaged for approximately half the original investment amount. Revenue for the next year is projected to be $800 million, and is expected to grow at an annual rate of 20% for four years (i.e., years 2 through 5), after which revenues are expected to remain at that level indefinitely. Annual variable costs and year-end net working capital associated with the project are estimated to be 30% and 10% of annual revenue respectively, and fixed costs are estimated to be $80 million per year.

Neither the debt nor equity of T. Holdings is traded, but S. Corp reckons they are worth $3 billion and $6 billion respectively. In the immediate future, T. Holdings intends to recapitalize by issuing equity to repay all of their outstanding debt. In addition, S. Corp looked into Good Inc. and Bad Inc.—the former is a conglomerate with businesses such as global telecommunications, food and beverage, and financial services, whereas the latter is a pure-play which focuses on developing their telecommunications business in the Asia- Pacific. Also, S. Corp provides the following information on these entities:

Good Inc.

Bad Inc.

Beta

1.80

1.20

Market value of equity

$10 billion

$4 billion

Market value of debt

$20 billion

$2 billion

Face value of debt

$22 billion

$2.2 billion

Years to debt maturity

15

5

Annual coupon rate

10%

8%

The prevailing corporate marginal tax rate is 20%, the expected return on the market portfolio is 15%, and the risk-free rate is 5%. Assume the firm’s cost of debt does not vary with capital structure and financial distress is costless.

  • (i) Calculate and justify a suitable weighted average cost of capital based on T. Holdings’ existing capital
  • Justify and calculate a suitable discount rate for the telecommunications project.
  • (i) Compute operating cash flows for the first five
  • Compute changes in net working capital for the first five
  • Compute NPV based on cash flow from assets for the first five
  • Should T. Holdings accept the telecommunicationsproject?

Debt-free, Inc., an unlevered firm, is planning to use debt in its capital structure. The firm currently has 5,000 shares outstanding trading at $60 per share. The firm plans to sell 150 6% annual-coupon, 10-year bonds at their face values of $1,000 each and use the proceeds to repurchase some of its shares. When the bonds mature, Debt-free, Inc. plans to reissue new bonds to pay off the principal and to “roll over” its debt this way indefinitely. Assume the firm’s cost of debt does not change and there are no costs of financial distress. Earnings before interest and tax are expected to remain at $28,000 per year forever and the firm has a dividend policy of paying out all of its earnings. Maureen currently owns 100 shares of Debt- free, Inc.

  • (i) Calculate the total dollar annual dividend Maureen receives under the firm’s existing capital
  • If the market learns of the capital restructuring before the exercise is completed, how many shares are repurchased under the planned capital restructuring?
  • Calculate total dollar annual dividend Maureen receives under the firm’s planned capital
  • Debt-free, Inc. completes its planned capital restructuring but Maureen prefers the annual dividend payout of the unlevered firm. What is Maureen’s cash flow from homemade leverage by referencing the levered firm’s capital structure and assuming that she can borrow and lend at the same rate as the firm?
  • Is capital structure irrelevant?
  • Redo part (a) assuming a one-tier corporate tax rate of 20% applies. Ignore personal income

Loan Calculation

Part A (i)

The interest that will be paid in first month of 25th year of loan is $ 705.6246.

The formula for computation of interest is IPMT(Rate, Per, Nper, PV, FV)

Accordingly, the formula put in was IPMT(0.036/12,289,360,-800000)

The solution that was arrived stands at $ 705.62

Part A (ii)

The total amount of interest that will be paid over the life of the loan is $509378.61.

Sl No

Particulars

Amount ($)

1

Loan amount

800000

2

Tenure

30 years

3

Saving Interest Rate

1.20%

4

Loan Interest rate

3.60%

5

Monthly EMI

3637.16

6

Total Amount of Emi

1309378.61

7

Interest

509378.61

The computation of Monthly EMI has been done by using the formula PMT(rate, nper,pv,fv)

Accordingly, the values have been put in PMT(0.036/12,360(12*30),-800000,0)

The value derived was $ 3637.16 per month EMI.

Further to compute the entire amount of EMI that has been paid, EMI has been multiplied by 360= 3637.16 *360=$1309378.61 and the interest amount that has been paid on principal has been derived by reducing the loan amount from the total EMI=

Total Emi-Principal Loan

1309378.61-800000= $5,09,378.61


Part B

The Principal amount of loan under the said programme is AUD 800,000 and interest on the same over the tenure of the loan i.e. 360 months is $5,09,378 roughly 63% of principal. Further, in case of repayment of loan initially the interest is set off and then principal leading to such huge interest on the loan over the tenure. It shall also be worthwhile to note that the amount of interest decreases over the tenure of the loan.

The above computation is based on the understanding that there are no prepayment of intention to set off the loan earlier. Further, the interest rate on such loan does not fluctuate over the period and borrower does not default the loan.

Part C

For computation of present value of the loan EMI paid over the period of 360 months have been discounted using the rate of 1.2% p.a. compounded monthly. Accordingly the formula used has been stated here-in-below:

T( Sigma)t=0= Cash flow/(1+r)t

Accordingly the present value of 1st  EMI has been calculated as =3637.16/(1+.012/12)^1

Last EMI = 3637.16/(1+.012/12)^360

The resulting value has been added to arrive at the value $ 1,09,9143.923. (Refer Excel for detailed computation)

Part D

The present value has been computed on the basis of time value of money and the rate used for discounting is rate for deposit which can be considered equivalent to risk free interest rate. Further, it shall be noted that loan repayment is inclusive of interest and principal.

The difference between the actual amount of loan granted and the present value of such loan is $ 2,99,143.9229 which represent that I am paying extra by taking the loan as the person who lent me the money has earned extra after considering the risk free rate of interest. The extra amount represent payment for undertaking risk.

WACC Calculation

The rational for such difference is use of lower discount rate i.e 1.2% instead of 3.6%. Thus, the difference is mainly on account of risk undertaken by the person lending the money.

Part A (i)

The computation of WACC is presented here-in-below:

  • Cost of Debt of the company before tax is 8%
  • Cost of the debt net of tax = 8%*(1-tax rate)=8%(1-20%)=6.4%
  • Risk Free Rate is 5%
  • Market Return is 15%
  • Risk Premium= Market Return- Risk Free Rate=15%-5%=10%
  • Beta of Bad Inc= 1.2

Since Beta Inc is similar to the tested company, Beta of asset of the same needs to be computed to derive the beta of the tested company:

Beta Asset-= Beta Equity/(1+ (1-tax)*Debt/Equity)

=1.2(1+(1+(1-0.2)*2/4)

=0.857

Beta of the tested company =

Beta of Equity = Beta of Asset *(1+ (1-tax)*Debt/Equity)

=0.857*(1+(1-0.2)*3/6)

=1.2

  • Cost of Equity = Risk Free Rate + Risk Premium* Beta of Equity

=5%+ 10% *1.2

 =17%

  • Weighted Average Cost of Capital of Company = (Cost of debt* weight of debt + Cost of equity* Weight of Equity)/ total weight

=(6.4%*3+ 17%*6)/9

=13.47%

Weighted Average Cost of capital

Sl NO

Particular

Cost

1

Cost of Debt

8%

2

Cost of Debt post tax

6.4%

3

Risk Free rate

5%

4

Market return

15%

5

Risk Premium

10%

6

Beta

1.20

7

Cost of Equity

17.00%

8

Weight of Debt

3.00

9

Weight of Equity

6

10

Weight of Debt

3

11

WACC

13.47%

Computation of beta

Sl NO

Particular

Cost

1

Beta Levered

1.2

2

Beta Unlevered

0.857142857

3

Beta of Proposed project

1.2

 

For computation of cost of equity, only Bad Inc. has been considered as Bad Inc. business is similar to that of the company being analysed. Thus, on the basis of same WACC has been estimated @13.47%.

Part A (ii)

The suitable discount rate is Weighted Average Cost of capital of the project i.e. 13.47% as the same justifies the require rate of return desired by the people who are financing the project. Thus, WACC shall serve the purpose of suitable discount rate below which the project shall not be accepted. (CFI Education Inc., 2018)

In addition, the above represents the hurdle rate and the minimum rate of return that shall be given to investor for the project to survive and continue. Thus, it shall be prudent to use this rate as the same represent reward for the risk undertaken by the investor,

Part B (i)

The operating cash flows of the project for the first five years have been detailed here-in-below:

Sl No

Particular

year 0

year 1

year 2

year 3

year 4

year 5

Terminal Value

1

Revenue

800

960

1152

1382.4

1658.88

2

Annual Working Cost (Variable)

-240

-288

-345.6

-414.72

-497.664

3

Fixed Cost

-80

-80

-80

-80

-80

4

Depreciation

-120

-120

-120

-120

-120

5

EBIT (1-2-3-4)

360

472

606.4

767.68

961.216

6

Tax (5*20%)

-72

-94.4

-121.28

-153.536

-192.2432

7

EBI (5-6)

288

377.6

485.12

614.144

768.9728

8

Depreciation

120

120

120

120

120

9

OCF

408

497.6

605.12

734.144

888.9728

  • Revenue for year 1 has been provided and from year 2 the same has been computed like

Year 1*1.2=800*1.2=960

Year 2*1.2=960*1,2=1152

…….

Year 4*1.2=1382.4*1.2=1658.88

  • Annual Working Cost or Variable cost has been computed in the following manner

Year 1= Revenue Year 1*30%=800*30%=240

Year 2= Revenue Year 2*30%=960*30%=288

Year 5= Revenue Year 5*30%=1658.88*30%=497.664

  • Fixed cost has been provided at $80.
  • Depreciation has been computed by allocating the plant cost over a period of 5 year i,e

600/5=120 every year

  • Earnings Before Interest and Tax has been computed by = Revenue-variable cost-fixed cost-depreciation

For year 1

= 800-240-80-120=$360

For other year similar calculation has been done.

  • Tax has been computed = EBIT*30%

For year 1

= $360*20%= $72

For other years similar computation has been done.

  • Operating Cash Flow = EBIT-Tax + Depreciation

For year 1

= $360-$72+$120=$408

For year 5

=961.216-192.2432+120=$888.9728

Part B(ii)

The change is working capital over next five years has been presented here-in- below:

Sl No

Particular

year 0

year 1

year 2

year 3

year 4

year 5

Terminal Value

1

Net Working Capital Level

80

96

115.2

138.24

165.888

2

Change in Net Working Capital

80

16

19.2

23.04

27.648

3

Net Cash flow from sale of Asset

240

4

Realisation of Net working capital at end

165.888

 


The said computation has been derived in the following manner:

  • Net Working Capital Level

For year 1 = Revenue for year 1*10%=800*10%=$80

For Year 5= Revenue for year 5*10%=1658.88*10%=$165.89

  • Change in Working Capital level

For year 1 = Working Capital Level in Year 1- Working Capital level in Year 0=80-0=$80

For year 2 = Working Capital Level in Year 2- Working Capital level in Year 1=90-80=$16

For year 5 = Working Capital Level in Year 5- Working Capital level in Year 4=165.88-138.24=$27.648

  • Net Cash flow from sale of Asset : Sale Value *(1-Tax Rate )

Projected Cash Flows and Financial Analysis for Project

=300*(1-20%) =$240

  • Realisation of Working Capital at the end of the project = Net Working Capital level at year 5 = $165.89

Part B(iii)

Sl No

Particular

year 0

year 1

year 2

year 3

year 4

year 5

Terminal Value

1

Infrastructural Investment

-600

2

Depreciation

-120

-120

-120

-120

-120

3

Salvage Value

240

4

Revenue

800

960

1152

1382.4

1658.88

5

Annual Working Cost

-240

-288

-345.6

-414.72

-497.664

6

Working Capital

-80

-16

-19.2

-23.04

-27.64

165.88

7

Fixed Cost

-80

-80

-80

-80

-80

8

Net Cash Flow

280

456

587.2

744.64

933.576

405.88

9

Tax

-72

-94.4

-121.28

-153.536

-192.2432

10

Cash Flow after Tax

208

361.6

465.92

591.104

741.3328

405.88

11

Depreciation

120

120

120

120

120

12

Cash Flow after Tax & Depreciation

328

481.6

585.92

711.104

861.3328

405.88

13

Discounting factor

1

0.881316

0.776718

0.684534

0.603291

0.53169003

0.53169003

14

Present Value of Cash flows

-600

289.0717

374.0674

401.0822

429.0026

457.9620621

215.8023493

15

Net Present Value

1566.988

Uptill cash flow after tax and depreciation computation has been detailed above

Post that the computation of  present value has been provided here-in-under:

Cash Flow at year 1 *(1/1+ WACC)=328*.881316=289.717

Cash Flow at year 2 *(1/(1+ WACC)^2)=328*.776718=374.067

Cash Flow at year 5 *(1/(1+ WACC)^5)=861.322*.53169=457.962

Further Net Present Value has been computed by using the formula=

Summation of Present value of csh flow form year 1 to terminal Value- Year 0=2166.988-600=$1566.88

Part B(iv)

Yes, the project shall be accepted based on quantitative analysis of the project as the Net Present value of project is $1567.651 at 13.47 % rate of discounting. Further, positive Net Present Value indicates that project is feasible.

PART A (i)

Sl No

Particulars

Quantity (a)

Rate (b)

Amount(C=a*b)

1

Share

5000

60

300000

2

10 Year Bond

150

1000

150000

3

Buy Back Shares

2500

60

150000

4

Cost of Debt before Tax

6%

5

Earnings Before Interest and Tax

28000

6

Tax Rate

NiL

7

Profit after Tax

28000

8

Dividend Per Share

5.6

9

Dividend received by Maureen

100

5.6

560

Answer (a(i))

The computation has been derived in the following manner

Earnings Before Interest and Tax = $28000

No of Shares=5000

Dividend per share=EBIT/No of shares=28000/5000= $5.6

No of Shares of Maureen=100

Dividend Received by Maureen= 100*$5.6= $560

Part A (ii)

Sl No

Particulars

Quantity (a)

Rate (b)

Amount(C=a*b)

1

Share

5000

60

300000

2

10 Year Bond

150

1000

150000

3

Buy Back Shares

2500

60

150000

4

Cost of Debt before Tax

6%

5

Earnings Before Interest and Tax

28000

6

Tax Rate

NiL

7

Profit after Tax

28000

8

Dividend Per Share

5.6

9

Dividend received by Maureen

100

5.6

560

10

Buy Back Shares

2500

60

150000

Answer (a(ii))

The detail of computation has been provided here-in-below:

Amount of debt issued= 150*1000=$150000

Share price=$60

No of share to be bought back=Debt/Share price=150000/60=2500

PART A (iii)

Sl No

Particulars

Quantity (a)

Rate (b)

Amount(C=a*b)

1

Share

5000

60

300000

2

10 Year Bond

150

1000

150000

3

Buy Back Shares

2500

60

150000

4

Cost of Debt before Tax

6%

5

Earnings Before Interest and Tax

28000

6

Tax Rate

NiL

7

Profit after Tax

28000

8

Dividend Per Share

5.6

9

Dividend received by Maureen

100

5.6

560

10

Buy Back Shares

2500

60

150000

11

Earnings Before Interest and Tax

28000

12

Interest (2*4)

9000

13

Profit after Tax (11-12)

19000

14

Dividend per share (13/3)

7.6

15

Dividend received by Maureen

100

7.6

760

Answer (a(iii))

The computation has been derived in the following manner

Earnings Before Interest and Tax = $28000

Interest= Debt Amount* 6%=150000*60%= $9000

Earning before Tax= EBIT-Interest=28000-9000=$19000

Dividend per share=EBIT/No of shares=19000/2500= $7.6

No of Shares of Maureen=100

Dividend Received by Maureen= 100*$7.6= $760

PART A (iv)

Sl No

Particulars

Amount

1

No of shares under existing Capital Structure

100

2

Proportion of debt in the capital structure of the company

50%

3

Total Capital of Maureen

6000

4

Total  value of shares to be sold

3000

5

Total debt to be let out (3-4)

3000

6

Receipt of dividend (50*7.6)

380

7

Interest (3000*6%)

180

8

Total Receipt (6+7)

560

The computation has been derived in the following manner

The proportion of debt in the capital of the company=Debt/ Total capital=1500000/300000=50%

Total Capital of Maureen = Number of Shares* Rate per share=100*60=$6000

Value of share to be sold to incorporate debt= Capital*50%=6000*50%=$3000

Interest on Debt =Debt Amount * Rate of Coupon=3000*6%=$180

Dividend Receipt= No of Shares* Dividend per share=50*7.6=$380

Total Receipt=Interest + dividend= $180+$380=$560

Part (v)

In terms of Modigliani Miller theory, capital structure is irrelevant and the value of the company is dependent on the net operating cash flow of the company. However, under such thesis there is no transaction cost and taxes. Further, if the environment compasses tax then the above proposition does not hold true as the value of the company is increased by the present value of tax benefit. Further, cost of equity of the company shall rise on account of debt in the capital structure in terms of MM Theory leasing to same WACC.

Part B  (i,ii &iii)

Sl No

Particulars

Quantity (a)

Rate (b)

Amount(C=a*b)

1

Share

5000

60

300000

2

10 Year Bond

150

1000

150000

3

Buy Back Shares

2500

60

150000

4

Cost of Debt before Tax

6%

5

Earnings Before Interest and Tax

28000

6

Tax Rate

20%

7

Profit after Tax

22400

8

Dividend Per Share

4.48

9

Dividend received by Maureen

100

4.48

448

10

Buy Back Shares

2500

60

150000

11

Earnings Before Interest and Tax

28000

12

Interest (2*4)

9000

13

Profit after Tax (11-12)*80%

15200

14

Dividend per share (13/3)

6.08

15

Dividend received by Maureen

100

6.08

608

The computation has been provided here-in-below:

Earnings Before Interest and Tax = $28000

Earning After Tax =EBIT*(1-Tax rate)=28000*(1-20%)= $22400

No of Shares=5000

Dividend per share=EBIT/No of shares=22400/5000= $4.48

No of Shares of Maureen=100

Dividend Received by Maureen= 100*$4.48= $448 (Answer)

Amount of debt issued=$150000

Share price=$60

No of share to be bought back=Debt/Share price=150000/60=2500 (Answer)

Interest= Debt Amount* 6%=150000*60%= $9000

Earning before Tax= EBIT-Interest=28000-9000=$19000

Earning After Tax= EBT*(1-Tax rate)=19000*(1-20%)= $15200

Dividend per share=EBIT/No of shares=15200/2500= $6.08

No of Shares of Maureen=100

Dividend Received by Maureen= 100*$6.08= $608(Answer)

PART B (iv)

Sl No

Particulars

Amount

1

No of shares under existing Capital Structure

100

2

Proportion of debt in the capital structure of the company

50%

3

Total Capital of Maureen

6000

4

Total  value of shares to be sold

3000

5

Total debt to be let out

3000

6

Receipt of dividend (50*6.08)

304

7

Interest (3000*6%)

180

8

Total Receipt (6+7)

484

The computation has been provided here-in-below:

The proportion of debt in the capital of the company=Debt/ Total capital=1500000/300000=50%

Total Capital of Maureen = Number of Shares* Rate per share=100*60=$6000

Value of share to be sold to incorporate debt= Capital*50%=6000*50%=$3000

Interest on Debt =Debt Amount * Rate of Coupon=3000*6%=$180

Dividend Receipt= No of Shares* Dividend per share=50*6.06=$304

Total Receipt=Interest + dividend= $180+$304=$484

PART B (v)

In terms of Modigliani Miller theory, capital structure is irrelevant and the value of the company is dependent on the net operating cash flow of the company. However, under such thesis there is no transaction cost and taxes. Further, if the environment compasses tax then the above proposition does not hold true as the value of the company is increased by the present value of tax benefit. Further, cost of equity of the company shall rise on account of debt in the capital structure in terms of MM Theory leasing to same WACC. (Study.com, 2018)

References:

CFI Education Inc. (2018). WACC. Retrieved October 3, 2018, from corporatefinanceinstitute.com: https://corporatefinanceinstitute.com/resources/knowledge/finance/what-is-wacc-formula/

Study.com. (2018). The Modigliani-Miller Theorem: Definition, Formula & Examples. Retrieved October 3, 2018, from Study.com: https://study.com/academy/lesson/the-modigliani-miller-theorem-definition-formula-examples.html

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