Problem 16-19 Using net present value and internal rate of return to evaluate in
ID: 2465139 • Letter: P
Question
Problem 16-19 Using net present value and internal rate of return to evaluate investment opportunities LO 16-2, 16-3
Pedro Spier, the president of Spier Enterprises, is considering two investment opportunities. Because of limited resources, he will be able to invest in only one of them. Project A is to purchase a machine that will enable factory automation; the machine is expected to have a useful life of four years and no salvage value. Project B supports a training program that will improve the skills of employees operating the current equipment. Initial cash expenditures for Project A are $200,000 and for Project B are $80,000. The annual expected cash inflows are $63,000 for Project A and $26,400 for Project B. Both investments are expected to provide cash flow benefits for the next four years. Spier Enterprises’ cost of capital is 8 percent. (PV of $1 and PVA of $1 ) (Use appropriate factor(s) from the tables provided.)
Pedro Spier, the president of Spier Enterprises, is considering two investment opportunities. Because of limited resources, he will be able to invest in only one of them. Project A is to purchase a machine that will enable factory automation; the machine is expected to have a useful life of four years and no salvage value. Project B supports a training program that will improve the skills of employees operating the current equipment. Initial cash expenditures for Project A are $200,000 and for Project B are $80,000. The annual expected cash inflows are $63,000 for Project A and $26,400 for Project B. Both investments are expected to provide cash flow benefits for the next four years. Spier Enterprises’ cost of capital is 8 percent. (PV of $1 and PVA of $1 ) (Use appropriate factor(s) from the tables provided.)
Explanation / Answer
a-1:
Net Present Value NPV = - C0 + C1/ (1+r) + C2/ (1+r)2 + . . . . + CT/ (1+r)T
Where C0 = Initial investment
C = Cash flow
T = Time = 4 years
r = cost of capital = 8% = 0.08
NPV of Project A = - $200,000 + $63,000/ (1 + 0.08) + $63,000/ (1 + 0.08)2 + 63,000/ (1 + 0.08)3 +
63,000/ (1 + 0.08)4
= - $200,000 + $58,333.33 + $54,012.35 + $50,011.43 + $46,306.88
= $8,663.99
NPV of Project B = - $80,000 + $ 26,400/ (1 + 0.08) + $26,400/ (1 + 0.08)2 + $26,400/ (1 + 0.08)3 + $26,400/ (1 + 0.08)4
= - $80,000 + $24,444.44 + $22,633.75 + $20,957.17 + $19,404.78
= $7,440.14
b:
The Internal rate of return (IRR) on a project is the rate of return at which the projects NPV equals zero.
- C0 + C1/ (1+IRR) + C2/ (1+ IRR)2 + . . . . + CT/ (1+ IRR)T = 0
For Project A:
Approximate IRR for project A = 9.93%
For Project B:
Let us assume that IRR = 10%
NPV of Project B @ IRR = 10%
Cash flow
Year
Denominator (1+ IRR)^T
Denominator Value
PV = [Cash flow/Denominator Value]
C0
-80,000.00
0
(1 + 0.1)^0
1
-80,000.00
C1
26,400.00
1
(1 + 0.1)^1
1.1
24,000.00
C2
26,400.00
2
(1 + 0.1)^2
1.21
21,818.18
C3
26,400.00
3
(1 + 0.1)^3
1.331
19,834.71
C4
26,400.00
4
(1 + 0.1)^4
1.4641
18,031.56
NPV =
3,684.45
Let us assume that IRR = 12%
NPV of Project B @ IRR = 12%
Cash flow
Year
Denominator (1+ IRR)^T
Denominator Value
PV = [Cash flow/Denominator Value]
C0
-80,000.00
0
(1 + 0.12)^0
1.0000
-80,000.00
C1
26,400.00
1
(1 + 0.12)^1
1.1200
23,571.43
C2
26,400.00
2
(1 + 0.12)^2
1.2544
21,045.92
C3
26,400.00
3
(1 + 0.12)^3
1.4049
18,791.00
C4
26,400.00
4
(1 + 0.12)^4
1.5735
16,777.68
NPV =
186.02
Let us assume that IRR = 12.11%
NPV of Project B @ IRR = 12.11%
Cash flow
Year
Denominator (1+ IRR)^T
Denominator Value
PV = [Cash flow/Denominator Value]
C0
-80,000.00
0
(1 + 0.122)^0
1.0000
-80,000.00
C1
26,400.00
1
(1 + 0.122)^1
1.1211
23,548.30
C2
26,400.00
2
(1 + 0.122)^2
1.2569
21,004.64
C3
26,400.00
3
(1 + 0.122)^3
1.4091
18,735.74
C4
26,400.00
4
(1 + 0.122)^4
1.5797
16,711.93
NPV =
0.61
Approximate IRR for project B = 12.11%
Let us assume that IRR = 10% NPV of Project A @ IRR = 10% Cash flow Year Denominator (1+ IRR)^T Denominator Value PV = [Cash flow/Denominator Value] C0 -2,00,000.00 0 (1 + 0.1)^0 1 -2,00,000.00 C1 63,000.00 1 (1 + 0.1)^1 1.1 57,272.73 C2 63,000.00 2 (1 + 0.1)^2 1.21 52,066.12 C3 63,000.00 3 (1 + 0.1)^3 1.331 47,332.83 C4 63,000.00 4 (1 + 0.1)^4 1.4641 43,029.85 NPV = -298.48 Let us assume that IRR = 9.9% NPV of Project A @ IRR = 9.9% Cash flow Year Denominator (1+ IRR)^T Denominator Value PV = [Cash flow/Denominator Value] C0 -2,00,000.00 0 (1 + 0.099)^0 1.0000 -2,00,000.00 C1 63,000.00 1 (1 + 0.099)^1 1.0990 57,324.84 C2 63,000.00 2 (1 + 0.099)^2 1.2078 52,160.91 C3 63,000.00 3 (1 + 0.099)^3 1.3274 47,462.16 C4 63,000.00 4 (1 + 0.099)^4 1.4588 43,186.68 NPV = 134.58 Let us assume that IRR = 9.93% NPV of Project A @ IRR = 9.93% Cash flow Year Denominator (1+ IRR)^T Denominator Value PV = [Cash flow/Denominator Value] C0 -2,00,000.00 0 (1 + 0.0993)^0 1.0000 -2,00,000.00 C1 63,000.00 1 (1 + 0.0993)^1 1.0993 57,309.20 C2 63,000.00 2 (1 + 0.0993)^2 1.2085 52,132.44 C3 63,000.00 3 (1 + 0.0993)^3 1.3285 47,423.31 C4 63,000.00 4 (1 + 0.0993)^4 1.4604 43,139.55 NPV = 4.50