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.
 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 201617 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, 201718, 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 201617 in midJanuary, 2018, and the dividend for 201718 in midJanuary, 2019.
In midJanuary, 2019, Jillian wishes to spend $100,000, which will include the cost of new furniture. How much can she consume in midJanuary, 2018 if the capital market offers an interest rate of 8% per year?
Income Estimations 

Year 
201617 
201718 
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 

20162017 
64000 
0 
5760 
69120 
54176.88 
14943.12 
20172018 
76800 
14943.12 
8256.88 
100000 
100000 
0 
 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)/(0.130.05)= 61.39
 This question relates to the time value of money and deferred annuities.
Colin Way is age 40 today and plane to retire on his 65^{th} 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 65^{th} 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?
Total fund Balance on his 65th Birthday 
20,78,981.89 

Required Amount 
20,00,000.00 
Hence, the surplus amount is $78981.89.
 Using the fund balance, Colin then wishes to commence a monthly pension payable by the fund starting one month after his 65^{th}birthday, and ending on his 85^{th} 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 85^{th} birthday?
The fund balance $ 78,981.89
The amount of monthly pension = $567.08
 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:
 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% 
 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
 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.
 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:
 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.
 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 (UDRLDR) 

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 (UDRLDR) 
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 
 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% 
 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 straightline 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 textbook, 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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