Question

King Company's required rate of return is 10%. The company is considering the purchase of three machines, as indicated below. Consider each machine independently. (Ignore income taxes in this problem.)

Machine A will cost $25,000 and will have a useful life of 15 years. Its salvage value will be $1,000 and cost savings are projected at $3,500 per year. Calculate the machine's net present value.

How much should King Company be willing to pay for Machine B if the machine promises annual cash inflows of $5,000 per year for eight years?

Machine C has a projected life of ten years. What is the machine's internal rate of return if it costs $31,296 and will save $6,000 annually in cash operating costs? Would you recommend to King Company to purchase Machine C? Explain.

Answer 1

Question Analysis

King Company

Required rate of return 10%

	Machinery A	Machinery B	Machinery C
Cost	$25,000		$31,296
Useful life	15 years	8 years	10 years
Salvage value	$1,000
Cash inflow(cost savings)	$3,500 per year	$5,000 per year	$6,000

Question 1: Calculate Machine A’s Net Present Value.

Question 2: How much should King Company be willing to pay for Machine B, if the machine promises annual cash inflows of $5,000 per year for eight years?

Question 3: What is the internal rate of return of Machine C

Question 4: Would you recommend to King Company to purchase Machine C? Explain.

Answers

Question 1: Calculate Machine A’s Net Present Value.

Present Value of a cash inflow = Rn/(1+i)^n

R = cash inflow

n = the year(1^st year, 2^nd year, n^th year)

i = rate of interest

Calculation of Net Present Value of Cash inflows – Machine A

Year	Cash inflow	Calculations	Net present value
1	3500	3500/(1.10^1)	3,181.82
2	3500	3500/(1.10^2)	2,892.56
3	3500	3500/(1.10^3)	2,629.60
4	3500	3500/(1.10^4)	2,390.55
5	3500	3500/(1.10^5)	2,173.22
6	3500	3500/(1.10^6)	1,975.66
7	3500	3500/(1.10^7)	1,796.05
8	3500	3500/(1.10^8)	1,632.78
9	3500	3500/(1.10^9)	1,484.34
10	3500	3500/(1.10^10)	1,349.40
11	3500	3500/(1.10^11)	1,226.73
12	3500	3500/(1.10^12)	1,115.21
13	3500	3500/(1.10^13)	1,013.83
14	3500	3500/(1.10^14)	921.66
15	3500	3500/(1.10^15)	837.87
15	1000 (salvage value)	1000/(1.10^15)	239.39
Total Present Value of Cash inflows			26,860.67

Net Present Value    = Total Present value of Cash inflow - Total present value of cash outflow

                                      =26,860.67-25,000 = 1,860.67

What do you come to know by this answer?

We invest $25,000 in the beginning of the first year. If we discount cash inflows for the fifteen years, the present value of all cash inflows including salvage value comes to   $ 26,860.67. It means the machinery A is worth purchasing because the Net Present Value is positive, that is $1,860.67

Question 2: How much should King Company be willing to pay for Machine B, if the machine promises annual cash inflows of $5,000 per year for eight years?

The amount that the company should pay for this machinery is decided after finding out the present value of all future cash inflows. The company should pay less than the total present value of all future cash inflows, so that the Net Present Value of cash inflows will be positive, which means company gets profit out of investing in machinery B.

Year	Cash inflow	Calculations	Net present value
1	5,000	5000/(1.10^1)	4,545.45
2	5,000	5000/(1.10^2)	4,132.23
3	5,000	5000/(1.10^3)	3,756.57
4	5,000	5000/(1.10^4)	3,415.07
5	5,000	5000/(1.10^5)	3,104.61
6	5,000	5000/(1.10^6)	2,822.37
7	5,000	5000/(1.10^7)	2,565.79
8	5,000	5000/(1.10^8)	2,332.54
Total Present Value of Cash inflows			26,674.63

As the total present value of cash inflows is $26,674.63, the company should pay less than this amount.

The company should not pay equal or more than this amount.

Because the company will not have any profit out of this investment if it pays equal amount to or more than the present value of future cash inflows.

Question 3: What is the internal rate of return of Machine C

First we must understand what Internal Rate of Return means. Internal rate of return is a rate of return in which total present value of future cash inflows is equal to the the total present value of cash outflows(investment). It means, at Internal Rate of Return, the Net Present Value is Zero.

Steps to calculate Internal Rate of Return(IRR)

1. To calculate IRR, guess any rate of return (for example 10%) and calculate total present value of cash inflows and calculate Net Present Value.

2. If Net Present Value is closer to Zero, the selected rate of return is Internal Rate of Return.

3. If Net Present Value is Greater than Zero, increase the rate and calculate Net Present value as in the first step.

4. If Net Present Value is still greater than Zero, increase the rate till the Net Present Value is equal to or closer to zero.

5. If Net Present Value is less than zero, decrease the rate of return and calculate Net Present value and see whether it is equal to or closer to Zero. if it is still less than zero, decrease the rate of return till Net Present Value becomes equal to or closer to Zero.

In our answer I checked 10%, 11%, 12%, 13%, 14%

I find at 14% , Net present value becomes zero. Let’s see how:

Year	Cash inflow	PV @10%	PV @11%	PV @12%	PV @13%	PV @14%
1	6,000	5,454.55	5,405.41	5,357.14	5,309.73	5,263.16
2	6,000	4,958.68	4,869.73	4,783.16	4,698.88	4,616.81
3	6,000	4,507.89	4,387.15	4,270.68	4,158.30	4,049.83
4	6,000	4,098.08	3,952.39	3,813.11	3,679.91	3,552.48
5	6,000	3,725.53	3,560.71	3,404.56	3,256.56	3,116.21
6	6,000	3,386.84	3,207.85	3,039.79	2,881.91	2,733.52
7	6,000	3,078.95	2,889.95	2,714.10	2,550.36	2,397.82
8	6,000	2,799.04	2,603.56	2,423.30	2,256.96	2,103.35
9	6,000	2,544.59	2,345.55	2,163.66	1,997.31	1,845.05
10	6,000	2,313.26	2,113.11	1,931.84	1,767.53	1,618.46
		36,867.40	35,335.39	33,901.34	32,557.46	31,296.69

At 14%, total present value of cash inflows = Total present value of cash outflows(investment)

That is, 31296 = 31296.69

Net Present Value is Zero (Present Value of cash inflows – present value of cash outflows)

Hence, The internal rate of return for Machine C is 14%

Question 4: Would you recommend to King Company to purchase Machine C? Explain.

• Yes. We can recommend the Company to purchase Machine C.
• Because, the company’s expected rate of return is 10%.
• But Machine C has an internal rate of return of 14%.
• That is 4% extra.
• The company can purchase Machine C without any hesitation