Investment and Project Analysis: A Finance Homework Assignment

This finance homework assignment presents two primary problems. The first problem focuses on calculating the amount needed to be deposited today to cover future education costs, considering inflation, interest rates on a Certificate of Deposit (CD), and a gift from an uncle. The solution involves calculating the future cost of education, the future value of the CD, and then determining the amount the uncle needs to contribute to cover the remaining costs. The second problem assesses two investment projects (A and B) using various financial metrics. The analysis includes calculating and comparing the payback period, Net Present Value (NPV), Internal Rate of Return (IRR), and Profitability Index for both projects. The solution explains each method and provides a recommendation on which project to select based on the results, while also explaining the limitations of payback period and IRR, and justifying the preference for NPV and Profitability Index in making the final investment decision.

(1)
Cost of education today = $20,000
Annual inflation rate = 4%
Cost of education after 3 years = 20000 (1 + 4%)^3
= $22,497.28
Amount deposited today in CD = $1,000
Interest rate p.a. on CD = 6%
Amount in CD after 3 years = 1000 (1 + 6%)^3
= $1,191.02
Interest rate p.a. on gift received from uncle = 10%
Time period (in years) = 3
Suppose the amount funded by uncle is A. Then,
A (1 + 10%)^3 + 1191.02 = $22,497.28
A (1 + 10%)^3 = 22497.28 - 1191.02
A (1.3310) = $21,306.26
A = 21306.26 / 1.3310
A = $16,007.71
He should deposit now $16,007.71 now to enter into the college 3 years later.
(2)

a)
Year
Cash flow
(A)
Cash flow
(B)
Cumulative Cash
flow (A)
Cumulative Cash
flow (B)
0 -$54,000 -$23,000 -$54,000 -$23,000
1 $12,700 $11,600 -$41,300 -$11,400
2 $23,200 $11,200 -$18,100 -$200
3 $27,600 $12,500 $9,500 $12,300
4 $46,500 $6,000 $56,000 $18,300
$56,000 $18,300
Payback period (A) = 2 + (18100 / 27600)
= 2.66
Payback period (B) = 2 + (200 / 12500)
= 2.02
Project with lower payback period should be selected. In the given case, payback period
for project B is less than that of project A. Therefore, as per payback period criteria,
project B should be selected.
b)
Year Cash flow (A) Cash flow (B) PVF @ 14% PV (A) PV (B)
0 -$54,000 -$23,000 1.0000 -$54,000 -$23,000
1 $12,700 $11,600 0.8772 $11,140 $10,175
2 $23,200 $11,200 0.7695 $17,852 $8,618
3 $27,600 $12,500 0.6750 $18,629 $8,437
4 $46,500 $6,000 0.5921 $27,532 $3,552
$56,000 $18,300 $21,153 $7,783
NPV (A) = $21,153
NPV (B) = $7,783
Project with higher NPV should be selected. In the given case, NPV of project A is higher
than that of project B. Therefore, as per NPV criteria, project A should be selected.
c)

Yea
r Cash flow (A) Cash flow (B)
0 -$54,000 -$23,000
1 $12,700 $11,600
2 $23,200 $11,200
3 $27,600 $12,500
4 $46,500 $6,000
$56,000 $18,300
IRR (A) = 28.50%
IRR (B) = 30.94%
Project with higher IRR should be selected. In the given case, IRR of project B is higher
than that of project A. Therefore, as per IRR criteria, project B should be selected.
d)
Year Cash flow (A) Cash flow (B) PVF @ 14% PV (A) PV (B)
0 -$54,000 -$23,000 1.0000 -$54,000 -$23,000
1 $12,700 $11,600 0.8772 $11,140 $10,175
2 $23,200 $11,200 0.7695 $17,852 $8,618
3 $27,600 $12,500 0.6750 $18,629 $8,437
4 $46,500 $6,000 0.5921 $27,532 $3,552
$56,000 $18,300 $21,153 $7,783
Profitability Index
= Present value of cash inflows / present value of cash outflows
Profitability Index (A) = 1.39
Profitability Index (B) = 1.34
Project with higher profitability index should be selected. In the given case, profitability
index of project A is higher than that of project B. Therefore, as per profitability index
criteria, project A should be selected.
e)

We should accept the decision made by NPV and Profitability Index. Both of these are
considered superior to IRR and Payback period. IRR and payback has some limitations as
given below.
Payback period suffers from following two limitations:
1. It ignores time value of money. Time value of money is very important concept which
should not be ignored.
2. It ignores cash flows occurring after the payback period. Not considering all cash flows
is another disadvantage of payback period.
IRR assumes that all cash flows are being reinvested at the same rate of IRR which is not
possible in real life. Therefore, decision of NPV is given the preference over IRR.
Because of above reason, we should select project A.