In: Finance
You are considering an investment in two projects, A and B. Both projects will cost $115,000, and the projected cash flows are as follows:
YEAR PROJECT A PROJECT B
1 $7,188 $51,750
2 $21,562 $38,812
3 $40,250 $28,750
4 $50,315 $21,563
5 $57,500 $14,375
Using Excel and show formulas
a. Assuming that the WACC is 9.4%, calculate the payback period, discounted payback period, NPV, PI, IRR, and MIRR. If the projects are mutually exclusive, which project should be selected?
b. Create an NPV profile chart for projects A and B. What is the exact crossover rate for these two projects?
(a): The answers are:
Payback | Discounted payback | NPV | PI | IRR | MIRR | |
Project A | 3.91 | 4.67 | 12,145.72 | 1.11 | 12.50 | 11.62 |
Project B | 2.85 | 3.88 | 10,916.75 | 1.09 | 13.95 | 11.40 |
Calculations:
Payback:
Year | A's cash flow | Cumulative cash flow of A | B's cash flow | Cumulative cash flow of B | |
0 | -115,000.00 | -115,000.00 | -115,000.00 | -115,000.00 | |
1 | 7,188.00 | -107,812.00 | 51,750.00 | -63,250.00 | |
2 | 21,562.00 | -86,250.00 | 38,812.00 | -24,438.00 | |
3 | 40,250.00 | -46,000.00 | 28,750.00 | 4,312.00 | |
4 | 50,315.00 | 4,315.00 | 21,563.00 | ||
5 | 57,500.00 | 14,375.00 |
A's payback = 3+(46000/50315) = 3.91 years
B's payback = 2+(24438/28750) = 2.85 years
Discounted payback:
Year | A's cash flow | 1+r | PVIF | A's discounted cash flow | Cumulative discounted cash flow of A | B's cash flow | B's discounted cash flow | Cumulative discounted cash flow of B |
0 | -115,000.00 | 1.094 | 1.0000 | -115,000.00 | -115,000.00 | -115,000.00 | -115,000.00 | -115,000.00 |
1 | 7,188.00 | 0.9141 | 6,570.38 | -108,429.62 | 51,750.00 | 47,303.47 | -67,696.53 | |
2 | 21,562.00 | 0.8355 | 18,015.84 | -90,413.78 | 38,812.00 | 32,428.84 | -35,267.69 | |
3 | 40,250.00 | 0.7637 | 30,740.71 | -59,673.07 | 28,750.00 | 21,957.65 | -13,310.04 | |
4 | 50,315.00 | 0.6981 | 35,125.96 | -24,547.11 | 21,563.00 | 15,053.58 | 1,743.55 | |
5 | 57,500.00 | 0.6381 | 36,692.83 | 12,145.72 | 14,375.00 | 9,173.21 |
A's discounted payback = 4+(24547.11/36692.83) = 4.67 years
B's discounted payback = 3+(13310.04/15053.58) = 3.88 years
NPV:
Year | A's cash flow | 1+r | PVIF | A's discounted cash flow | B's discounted cash flow |
0 | -115,000.00 | 1.094 | 1.0000 | -115,000.00 | -115,000.00 |
1 | 7,188.00 | 0.9141 | 6,570.38 | 47,303.47 | |
2 | 21,562.00 | 0.8355 | 18,015.84 | 32,428.84 | |
3 | 40,250.00 | 0.7637 | 30,740.71 | 21,957.65 | |
4 | 50,315.00 | 0.6981 | 35,125.96 | 15,053.58 | |
5 | 57,500.00 | 0.6381 | 36,692.83 | 9,173.21 | |
NPV | 12,145.72 | 10,916.75 |
PI: PI = present value of cash inflows/present value of cash outflows
A's cash flow | 1+r | PVIF | A's discounted cash flow | B's discounted cash flow |
-115,000.00 | 1.094 | 1.0000 | -115,000.00 | -115,000.00 |
7,188.00 | 0.9141 | 6,570.38 | 47,303.47 | |
21,562.00 | 0.8355 | 18,015.84 | 32,428.84 | |
40,250.00 | 0.7637 | 30,740.71 | 21,957.65 | |
50,315.00 | 0.6981 | 35,125.96 | 15,053.58 | |
57,500.00 | 0.6381 | 36,692.83 | 9,173.21 | |
Present value of inflows | 127,145.72 | 125,916.75 | ||
Present value of outflow | 115,000.00 | 115,000.00 | ||
PI | 1.11 | 1.09 |
IRR: it is the rate that makes NPV as nil:
A's cash flow | 1+r | PVIF | A's discounted cash flow |
-115,000.00 | 1.1250402 | 1.0000 | -115,000.00 |
7,188.00 | 0.8889 | 6,389.11 | |
21,562.00 | 0.7901 | 17,035.43 | |
40,250.00 | 0.7023 | 28,265.83 | |
50,315.00 | 0.6242 | 31,406.92 | |
57,500.00 | 0.5548 | 31,902.72 | |
NPV | 0.00 |
B's IRR:
Year | 1+r | PVIF | B's cash flow | B's discounted cash flow |
0 | 1.139537 | 1.0000 | -115,000.00 | -115,000.00 |
1 | 0.8775 | 51,750.00 | 45,413.18 | |
2 | 0.7701 | 38,812.00 | 29,888.84 | |
3 | 0.6758 | 28,750.00 | 19,429.09 | |
4 | 0.5930 | 21,563.00 | 12,787.79 | |
5 | 0.5204 | 14,375.00 | 7,481.10 | |
Total | 0.00 |
MIRR: Present value of cash outflow = Terminal value/(1+MIRR)^5
Terminal value of A = 7188*1.094^4 + 21562*1.094^3 + 40250*1.094^2 + 50315*1.094^1 + 57500 = 199,245.43
or 115,000 = 199245.43/(1+MIRR)^5. Solving this we get MIRR = 11.62%
For B: Terminal value = 51750*1.094^4+38812*1.094^3 + 28750*1.094^2 + 21563*1.094^1 + 14375 = 197,319.56
or 115,000 = 197319.56/(1+MIRR)^5. Solving we get MIRR = 11.40%
(b) Exact cross over rate is the rate at which NPV is same for both the projects. The cross over rate is = 10.1883% or 10.19% (rounded off to 2 decimal place)
Graph:
60,000.00 50,000.00 As NPV 30,000.00 10,000.00 0.00 0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00