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## Question

You are required to complete this Assignment in Groups of 2 or 3 or 4 people. Groups of 1 or more than 4 persons will incur a penalty of 5 marks out of 30%.

All members of the Group should come from the same Tutorial class. You may consult and discuss the Assignment topic with others, but you must write up your answers yourselves. Penalties for copying and plagiarism are severe.

Ram Shack Ltd has just paid a dividend of \$3.00 a share. Investors require a 13% per annum return on investments such as Ram Shack. What would a share in Ram Shack Ltd be expected to sell for today (January, 2018) if the dividend is expected to increase by 20% in January, 2019, 16% in January, 2020, 12% in January, 2021 and thereafter by 5 per cent a year forever, from January, 2022 onwards?

This question relates to the time value of money and deferred annuities.

Colin Way is age 40 today and plane to retire on his 65th birthday. With future inflation, Colin estimates that he will require around \$2,000,000 at age 65 to ensure that he will have a comfortable life in retirement. He believes that he can contribute \$3,000 at the end of each month, starting in one months’ time and finishing on his 65th birthday.

If the fund to which he contributes earns 6% per annum, compounded monthly (after tax), how much will he have at age 65? Will he have achieved his targeted sum? What is the surplus or the shortfall?

Using the fund balance, Colin then wishes to commence a monthly pension payable by the fund starting one month after his 65th birthday, and ending on his 85th birthday, after which he expects that the fund will be fully expended. If the fund continues to earn the above return of 6% per annum, compounded monthly, how much monthly pension will Colin receive, if the fund balance reduces to zero as planned after the last pension payment on his 85th birthday?

Ray and Betty Read wish to borrow \$600,000 to buy a home. The loan from Battlers Bank requires equal monthly repayments over 20 years, and carries.an interest rate of 4.8% per annum, compounded monthly. The first repayment is due at the end of the first month.

i)the effective annual interest rate on the above loan.

ii)the amount of the monthly repayment (consisting of interest and principal repayment components) if the same amount is to be repaid every month over the 20 year period of the loan.

iii)the amount of \$X, if - instead of the above - Battlers Bank agrees that Ray and Betty will repay the loan by paying the bank \$3,300 per month for the first 12 months, then \$3,750 a month for the next 12 months, and after that \$X per month for the balance of the 20 year term.

iv)how long (in years and months) it would take to repay the loan if, alternatively, Ray and Betty decide to repay \$3,500 per month, with the first repayment again being at the end of the first month after taking the loan, and continuing until the loan was repaid.

v)under option iv) above, the amount of the final repayment. [NOTE: Towards  the end of the loan repayment period, after the final full monthly instalment of \$3,500 is paid, a lesser amount is likely to be outstanding. That amount, plus interest to the end of the following month, is the final loan repayment amount.]

i)If the cash flows after year 0 occur evenly over each year, what is the payback period for each project, and on this basis, which project would you prefer?

ii)Would the payback periods then be any different to your answer in i)? If so, what would the payback periods be?

iii)Sketch freehand the net present value (NPV) profiles for each investment on the same graph. Label both axes and the NPV profile for each investment.

iv)Calculate the internal rate of return (IRR) for each project and indicate them on the graph.

v)Calculate the exact crossover point and indicate it on the above graph.

vi)State which of the investments you would prefer, depending on the required rate of return (i.e., depending on the discount rate).

Diana Deall Ltd is considering the purchase of new technology costing \$700,000, which it will fully finance with a fixed interest loan of 10% per annum, with the principal repaid at the end of 4 years.

Diana Deall Ltd’s cost of capital is 12%. The tax rate is 30%. Tax is paid in the year in which earnings are received.

(a)Calculate the net present value (NPV), that is, the net benefit or net loss in present value terms of the proposed purchase costs and the resultant incremental cash flows.

(b)Should the company purchase the technology? State clearly why or why not.

Question
1. This is a two period certainty model problem.

Assume that Jillian Black has a sole income from Halcyon Ltd in which she owns 10% of the ordinary share capital.

In its financial year 2016-17 just ended, Halcyon Ltd reported net profits after tax of \$800,000, and announced its net profits after tax expectation for the next financial year, 2017-18, to be 20% higher than this year’s figure. The company operates with a dividend payout ratio of 80%, which it plans to continue, and will pay the annual dividend for 2016-17 in mid-January, 2018, and the dividend for 2017-18 in mid-January, 2019.

In mid-January, 2019, Jillian wishes to spend \$100,000, which will include the cost of new furniture. How much can she consume in mid-January, 2018 if the capital market offers an interest rate of 8% per year?

 Income Estimations Year 2016-17 2017-18 Net Profit 800000 960000 Dividend Payout 80% 80% Dividend 640000 768000 Equity holding of Jillian Black 10% 10% Dividend of Jillian Black 64000 76800
 Two period Certainty problem Year Income Opening Amount Interest Consumption Balance 2016-2017 64000 0 5760 69120 54176.88 14943.12 2017-2018 76800 14943.12 8256.88 100000 100000 0
1. This question relates to the valuation of shares.

Ram Shack Ltd has just paid a dividend of \$3.00 a share. Investors require a 13% per annum return on investments such as Ram Shack. What would a share in Ram Shack Ltd be expected to sell for today (January, 2018) if the dividend is expected to increase by 20% in January, 2019, 16% in January, 2020, 12% in January, 2021 and thereafter by 5 per cent a year forever, from January, 2022 onwards?

 Year Dividend PVF @ 13% PV of Dividend 2018 3.00 0.885 2.655 2019 3.60 0.783 2.819 2020 4.18 0.693 2.894 2021 4.68 0.613 2.869 2022 61.39* 0.543 33.319 Price of Share 44.555

* 4.68 x (1+0.05)/(0.13-0.05)= 61.39

1. This question relates to the time value of money and deferred annuities.

Colin Way is age 40 today and plane to retire on his 65th birthday. With future inflation, Colin estimates that he will require around \$2,000,000 at age 65 to ensure that he will have a comfortable life in retirement. He believes that he can contribute \$3,000 at the end of each month, starting in one months’ time and finishing on his 65th birthday.

1. If the fund to which he contributes earns 6% per annum, compounded monthly (after tax), how much will he have at age 65? Will he have achieved his targeted sum? What is the surplus or the shortfall?
 Total fund Balance on his 65th Birthday 20,78,981.89 Required Amount 20,00,000.00

Hence, the surplus amount is \$78981.89.

1. Using the fund balance, Colin then wishes to commence a monthly pension payable by the fund starting one month after his 65thbirthday, and ending on his 85th birthday, after which he expects that the fund will be fully expended. If the fund continues to earn the above return of 6% per annum, compounded monthly, how much monthly pension will Colin receive, if the fund balance reduces to zero as planned after the last pension payment on his 85th birthday?

The fund balance \$ 78,981.89

The amount of monthly pension = \$567.08

1. This question relates to loan repayments and loan terms.

Ray and Betty Read wish to borrow \$600,000 to buy a home. The loan from Battlers Bank requires equal monthly repayments over 20 years, and carries.an interest rate of 4.8% per annum, compounded monthly. The first repayment is due at the end of the first month.

You are required to calculate:

1. The effective annual interest rate on the above loan.
 Nominal Interest rate 0.048 Monthly Interest Rate 0.004 Effective Interest Rate (1+r/n)^n Effective Interest Rate 4.91%
1. the amount of the monthly repayment (consisting of interest and principal repayment components) if the same amount is to be repaid every month over the 20 year period of the loan.
 Installment= Loan Amount/(1+r)^240 Loan 6,00,000.00 R 0.004 Installment= 3,893.74
• the amount of \$X, if - instead of the above - Battlers Bank agrees that Ray and Betty will repay the loan by paying the bank \$3,300 per month for the first 12 months, then \$3,750 a month for the next 12 months, and after that \$X per month for the balance of the 20 year term.

The revised loan amount to be taken for calculating the amount of X will be \$ 570184.82 and interest rate will be 4.8%.

Amount of installment= \$ 570184.82/ Cumulative present value factor @   4.8%

The amount of X= 570184.82/ 144.45

Hence X= 3,947.28

1. how long (in years and months) it would take to repay the loan if, alternatively, Ray and Betty decide to repay \$3,500 per month, with the first repayment again being at the end of the first month after taking the loan, and continuing until the loan was repaid.

Loan amount: \$600000

Installment= \$3500/Month

Interest= 4.8%

Hence, the no. of years required to repay the loan= 24.17 years

We can say 24 Years and 2 months.

1. under option iv) above, the amount of the final repayment. [NOTE: Towards  the end of the loan repayment period, after the final full monthly instalment of \$3,500 is paid, a lesser amount is likely to be outstanding. That amount, plus interest to the end of the following month, is the final loan repayment amount.]
 The extra amount to be paid over and above the loan amount is \$ 204.23 Hence, the amount of final repayment \$ 6,00,204.23

This question relates to alternative investment choice techniques

Laurel Hardy is considering the following cash flows for two mutually exclusive projects.

You are required to answer the following questions:

1. If the cash flows after year 0 occur evenly over each year, what is the payback period for each project, and on this basis, which project would you prefer?
 Year Cash Flows X Cash Flows Y 0 -42000 -42000 1 12000 18000 2 18000 18000 3 27000 18000 As given in the question the cash flows occur evenly. So, we take the average of cash flows for project X and project Y cash flows are already even. Average = (12000+18000+27000)/3 57000 Average Cash flows 19000 Payback Period(Years) 2.21 2.33 Hence, project X will be preferred over project Y.

IN THE REMAINING PARTS, ASSUME THAT ALL CASH FLOWS OCCUR AT THE END OF EACH YEAR.

1. Would the payback periods then be any different to your answer in i)? If so, what would the payback periods be?
 Year Cash Flows X Cumulative Cash Flows Cash Flows Y 0 -42000 -42000 -42000 1 12000 -30000 18000 2 18000 -12000 18000 3 27000 15000 18000 Payback Period(Years) 2.44 2.33 In this case the cash flows are even and hence, the payback period of project X increased.
• Sketch freehand the net present value (NPV) profiles for each investment on the same graph. Label both axes and the NPV profile for each investment.
 Discounting Rate NPV(X) NPV(Y) 0% 15,000.00 12,000.00 2% 12,508.45 9,909.90 4% 10,183.38 7,951.64 6% 8,010.41 6,114.22 8% 5,976.68 2,763.34 10% 4,070.62 1,232.96 12% 2,281.84 1,232.96 14% 600.96 -210.62 16% -980.48 -1,573.99 18% -2,470.16 -2,863.09 20% -3,875.00 -4,083.33 22% -5,201.33 -5,239.65 24% -6,454.87 -6,336.54 26% -7,640.86 -7,378.11 28% -8,764.07 -8,368.10 30% -9,828.86 -9,309.97

Calculate the internal rate of return (IRR) for each project and indicate them on the graph. [NOTE: It is satisfactory if the approximate IRR is calculated for Investment X by trial and error, and stated as a percentage correct to the nearer whole number. The IRR for Investment Y should be calculated as a percentage exactly, correct to 1 decimal place.]

 Project X Year Cash Flows PVF @ 14% PV PVF @ 15% PV PVF @ 14.75% PV 0 -42000 1.000 -42000.00 1.000 -42000.00 1.000 -42000.00 1 12000 0.877 10526.32 0.870 10434.78 0.871 10457.89 2 18000 0.769 13850.42 0.756 13610.59 0.759 13670.94 3 27000 0.675 18224.23 0.658 17752.94 0.662 17871.16 NPV 600.962 -201.693 0.00
 IRR= LDR+ NPV at LDR x     (UDR-LDR) NPV at LDR- NPV at UDR IRR= 14.75% Project Y Year Cash Flows PVF @ 13% PV PVF @ 14% PV PVF @ 13.7% PV 0 -42000 1.000 -42000.00 1.000 -42000 1.000 -42000 1 18000 0.885 15929.20 0.877 15789.474 0.880 15831.13 2 18000 0.783 14096.64 0.769 13850.416 0.774 13923.6 3 18000 0.693 12474.90 0.675 12149.487 0.680 12245.91 NPV 500.75 -210.6235 1
 IRR= LDR+ NPV at LDR x     (UDR-LDR) NPV at LDR- NPV at UDR IRR= 13.7%
 IRR Table IRR NPV(X) NPV(Y) 13% 1428.464 500.747 13.70% 846.558 0.647 14% 600.962 -210.624 14.75% 0.000 -728.107 15% -201.693 -901.948
1. Calculate the exact crossover point and indicate it on the above graph.
 Calculation of Crossover Point Year Project X Cash Flows Project Y Cash Flows Difference 0 -42000 -42000 0 1 12000 18000 -6000 2 18000 18000 0 3 27000 18000 9000 Crossover Point 22.47%
1. State which of the investments you would prefer, depending on the required rate of return (i.e., depending on the discount rate).

We would prefer Project X over Project Y as the NPV of project X is higher than the NPV of Project Y.

This question relates to capital budgeting.

Diana Deall Ltd is considering the purchase of new technology costing \$700,000, which it will fully finance with a fixed interest loan of 10% per annum, with the principal repaid at the end of 4 years.

The new technology will permit the company to reduce its  to reduce its labour costs by \$250,000 a year for 4 years, and the technology may be depreciated for tax purposes by the straight-line method to zero over the 4 years. The company thinks that it can sell the technology at the end of 4 years for \$40,000.

The technology will need to be stored in a building, currently being rented out for \$35,000 a year under a lease agreement with 4 yearly rental payments to run, the next one being due at the end of one year. Under the lease agreement, Diana Deall Ltd can cancel the lease by paying the tenant (now) compensation equal to one year’s rental payment plus 10%, but this amount is not deductible for income tax purposes.

This is not the first time that the company has considered this purchase. Twelve months ago, the company engaged Fairgo Consultants, at a fee of \$25,000 paid in advance, to conduct a feasibility study on savings strategies and Fairgo made the above recommendations. At the time, Diana Deall did not proceed with the recommended strategy, but is now reconsidering the proposal.

Diana Deall further estimates that it will have to spend \$30,000 in 2 years’ time overhauling the technology.  It will also require additions to current assets of \$40,000 at the beginning of the project, which will be fully recoverable at the end of the fourth year.

Diana Deall Ltd’s cost of capital is 12%. The tax rate is 30%. Tax is paid in the year in which earnings are received.

REQUIRED:

• Calculate the net present value (NPV), that is, the net benefit or net loss in present value terms of the proposed purchase costs and the resultant incremental cash flows.

[HINT: As shown in the text-book, it is recommended that for each year you calculate the tax effect first, then identify the cash flows, then calculate the overall net present value.]

 Year Labour Cost Depreciation Overhauling Cost Interest PBT Tax @ 30% PAT Cash Flows PVF @ 12% PV 0 -740000 1 -740000 1 250000 165000 0 70000 15000 4500 10500 175500 0.893 1,56,696.43 2 250000 165000 30000 70000 -15000 -4500 -10500 154500 0.797 1,23,166.45 3 250000 165000 0 70000 15000 4500 10500 175500 0.712 1,24,917.43 4 250000 165000 0 70000 15000 4500 10500 175500 0.636 1,11,533.42 4 Resale Value net of Tax 28000 0.636 17,794.51 4 Working capital 40000 0.636 25,420.72 NPV -1,80,471.03

Notes:

 Cost of technology 700000 Resale value 40000 Depreciation 165000 Interest 70000 Initial Investment Cost of Technology 700000 Add: Working Capital 40000 Initial Investment 740000
• Should the company purchase the technology? State clearly why or why not.

The company should not purchase the technology as the NPV of the investment is negative that means it is not profitable to invest in the project.

References:

Erickson, K. H. (2013). Investment Appraisal: A Simple Introduction, K. H. Erickson.

Herbst, A. F. (2003). Capital asset Investment: Strategy, Tactics and Tools, John Wiley & Sons, England.

Osborne, M. (2014). Multiple Interest Rate Analysis: Theory and Applications, Springer.

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