Finance Assignment: Time Value Of Money, Investment Evaluation, And Loan Repayment

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 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.

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 65^thbirthday, 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

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.