Question

Q1. (CLO3) All techniques with NPV profile—Mutually exclusive projects Fitch Industries is in the process of choosing the better of two equal-risk, mutually exclusive capital expenditure projects—M and N. The relevant cash flows for each project are shown in the following table. The firm’s cost of capital is 14%.

	Project M	Project N
Initial investment	$28,500	$27,000
1	$10,000	$11,000
2	$10,000	$10,000
3	$10,000	9,000
4	$10,000	8,000

a. Calculate each project’s payback period.

b. Calculate the net present value (NPV) for each project.

c. Calculate the profitability Index for the two projects.

d. Summarize the preferences dictated by each measure you calculated, and indicate which project you would recommend. Explain why?

Q2. (CLO3) Future values of annuities Ramesh Abdul wishes to choose the better of two equally costly cash flow streams: annuity X and annuity Y. X is an annuity due with a cash inflow of $9,000 for each of 6 years. Y is an ordinary annuity with a cash inflow of $10,000 for each of 6 years. Assume that Ramesh can earn 15% on his investments.

a. On a purely subjective basis, which annuity do you think is more attractive? Why?

b. Find the future value at the end of year 6 for both annuities.

c. Use your finding in part b to indicate which annuity is more attractive. Why? Compare your finding to your subjective response in part a.

Q3: Joan Messineo borrowed $15,000 at a 14% annual rate of interest to be repaid over 3 years. The loan is amortized into three equal, annual, end-of-year payments.

a. Calculate the annual, end-of-year loan payment.

b. Prepare a loan amortization schedule showing the interest and principal breakdown of each of the three loan payments.

c. Explain why the interest portion of each payment declines with the passage of time.

Answer 1

1)

a) Payback period

Project M

Statement showing cummulative cash flow

Year	Cash flow	Cummulative cash flow
1	10000	10000
2	10000	20000
3	10000	30000
4	10000	40000

Now we can use interpolation to find payback period

Year	Cummulative cash flow
2	20000
3	30000
1	10000
?	8500

= 8500/10000

=0.85

Thus payback period = 2+0.85 = 2.85 years

Project N

Statement showing cummulative cash flow

Year	Cash flow	Cummulative cash flow
1	11000	11000
2	10000	21000
3	9000	30000
4	8000	38000

Now we can use interpolation to find payback period

Year	Cummulative cash flow
2	21000
3	30000
1	9000
?	6000

=6000/9000

=0.67

Thus payback period = 2+0.67 = 2.67 years

b) NPV

Project M

Statement showing NPV

Year	Cash flow	PVIF @14%	PV
1	10000	0.8772	8771.93
2	10000	0.7695	7694.68
3	10000	0.6750	6749.72
4	10000	0.5921	5920.80
PV of cash Inflow	29137.12
Less : Initial Investment	28500.00
NPV	637.12

Here NPV = 637.12$

Project N

Statement showing NPV

Year	Cash flow	PVIF @14%	PV
1	11000	0.8772	9649.12
2	10000	0.7695	7694.68
3	9000	0.6750	6074.74
4	8000	0.5921	4736.64
PV of cash Inflow	28155.18
Less : Initial Investment	27000.00
NPV	1155.18

Here NPV = 1155.18$

c) Profitability Index

Profitability Index = PV of cash inflow/PV of cash outflow

Project M = 29137.12/28500 = 1.02

Project N = 28155.18/27000 = 1.04

d) Project N should be selected as it has higher NPV and PI and it has lower Payback period than project M

2)

a) on subjective basis annuity Y looks attractive as it has annuity of $10,000

b) Statement showing FV of annuity  X

Year	Cash flow	FVIF @15%	PV
0	9000	2.3131	20817.55
1	9000	2.0114	18102.21
2	9000	1.7490	15741.06
3	9000	1.5209	13687.88
4	9000	1.3225	11902.50
5	9000	1.1500	10350.00
6		1.0000	0.00
FV of cash Inflow	90601.19

Thus FV of X annuity = 90601.19$

Statement showing FV of annuity Y

Year	Cash flow	FVIF @15%	PV
0	0	2.3131	0.00
1	10000	2.0114	20113.57
2	10000	1.7490	17490.06
3	10000	1.5209	15208.75
4	10000	1.3225	13225.00
5	10000	1.1500	11500.00
6	10000	1.0000	10000.00
FV of cash Inflow	87537.38

Thus FV of Y annuity = 87537.38$

c) Annuity  X is more attractive if we go by the result obtained in (b). This is because obe installment in annuity X was received today hence it was able to earn more interest. As compared to ans in (a) , answer in (c) is different because of time value of money

3)

a) Installment = Loan amount/PVIFA(r%,n)

r = required rate = 14%

n = no of years = 3

Loan amount = $15,000

PVIFA(YTM%,n) = [1-(1/(1+r)^n / r ]
PVIFA(14%,3) = [1-(1/(1+14%)^3 / 14%]
=[1-(1/(1+0.14)^3 / 0.14]
=[1-(1/(1.14)^3 / 0.14]
=[1-0.6750 / 0.14]
=0.3250/0.14
=2.3216

Thus Installment = 15000/2.3216

=6460.97$

b) Statement showing Amortization schedule

			Towards
Year	Opening balance	Installment	Interest @ 14%	Principal	Closing balance
	A	B	C = A x 14%	D	E = A-D
1	15000	6461	2100	4361	10639
2	10639	6461	1489	4972	5668
3	5668	6461	793	5668	0

c) Interest portion is decreasing as some portion of installments goes to reduce outstanding loan amount.