Chapter 16, Problem 21P

Problem 10-21A Using net present value and payback period to evaluate investment opportunities

Daryl Kearns saved $240,000 during the 30 years that he worked for a major corporation. Now he has retired at the age of 60 and has begun to draw a comfortable pension check every month. He wants to ensure the financial security of his retirement by investing his savings wisely and is currently considering two investment opportunities. Both investments require an initial payment of $160,000. The following table presents the estimated cash inflows for the two alternatives:

Mr. Kearns decides to use his past average return on mutual fund investments as the discount rate; it is 8 percent.

Required

Round your computation to two decimal points.

1. a. Compute the net present value of each opportunity. Which should Mr. Kearns adopt based on the net present value approach?
2. b. Compute the payback period for each project. Which should Mr. Kearns adopt based on the payback approach?
3. c. Compare the net present value approach with the payback approach. Which method is better in the given circumstances?

To determine

Ascertain the net present value of each opportunity, and state whether person K should approve the given project or not.

Explanation of Solution

Net present value method:

Net present value method is the method which is used to compare the initial cash outflow of investment with the present value of its cash inflows. In the net present value, the interest rate is desired by the business based on the net income from the investment, and it is also called as the discounted cash flow method.

Ascertain the net present value of each opportunity, and state whether person K should approve the given project or not as follows:

Opportunity 1:

Net present value of opportunity 1
Year	Net cash flow (A)	Present value of $1 at 8% [from table 1 in appendix ](B)	Present value of net cash flow $\left(A\times B\right)$
1	$44,000	0.925926	$40,740.74
2	$47,200	0.857339	$40,466.40
3	$63,200	0.793832	$50,170.18
4	$80,000	0.735030	$58,802.40
Total present value of cash flows			$190,179.73
Less: Cost of investment			$160,000.00
Net present value of the project			$ 30,179.73

Table (1)

Opportunity 2:

Net present value of opportunity 2
Year	Net cash flow (A)	Present value of $1 at 8% [from table 1 in appendix ](B)	Present value of net cash flow $\left(A\times B\right)$
1	$81,600	0.925926	$75,555.56
2	$86,400	0.857339	$74,074.09
3	$16,000	0.793832	$12,701.31
4	$16,000	0.735030	$11,760.48
Total present value of cash flows			$174,091.44
Less: Cost of investment			$160,000.00
Net present value of the project			$14,091.44

Table (2)

In this case, opportunity 1is better for the investment, because opportunity 1 ($30,179.73) has higher net present value than opportunity 2 ($14,091.44).

To determine

Compute the payback period for each project, and state whether person K should approve the given project or not.

Explanation of Solution

Payback period: Payback period is the expected time period which is required to recover the cost of investment. It is one of the capital investment method used by the management to evaluate the proposal of long-term investment (fixed assets) of the business.

Compute the payback period for each project, and state whether person K should approve the given project or not as follows:

Opportunity 1:

Cash payback period of opportunity 1
Years and months	Net cash flows ($)	Cumulative net cash flows ($)
1	44,000	44,000
2	47,200	91,200
3	63,200	154,400
1 month (1)	5,600	160,000

Hence, the cash payback period of opportunity 1 is 3 years and 1 month.

Opportunity 2:

Cash payback period of opportunity 2
Year and months	Net cash flows	Cumulative net cash flows
1	81,600	81,600
11 months (2)	78,400	160,000

Hence, the cash payback period of opportunity 2 is 1 year and 11 months.

In this case, opportunity 2 is better for the investment, because opportunity 2 has shorter payback period than opportunity 1.

Working note:

Calculate the number of months in the cash payback period of opportunity 1:

$\begin{array}{c}\begin{array}{l}\text{Number of }\\ \text{months}\end{array}\}\text{ = }\left(\frac{\text{Balance amount of intital investment}}{\text{Total cash flow for particular year}}\right)\times \text{Number of months in a year}\\ \text{=}\frac{\$5,600}{\$80,000}\times 12\text{ months}\\ \text{=0}\text{.84}\\ \text{= 1 month}\end{array}$ (1)

Calculate the number of months in the cash payback period of opportunity 2:

$\begin{array}{c}\begin{array}{l}\text{Number of }\\ \text{months}\end{array}\}\text{ = }\left(\frac{\text{Balance amount of intital investment}}{\text{Total cash flow for particular year}}\right)\times \text{Number of months in a year}\\ \text{=}\frac{\$78,400}{\$86,400}\times 12\text{ months}\\ \text{=10}\text{.89}\\ \text{= 11 months}\end{array}$ (2)

To determine

Compare the net present value approach will the payback approach, and state the method which is better for the given circumstance.

Explanation of Solution

Compare the net present value approach will the payback approach, and state the method which is better for the given circumstance as follows:

The net present value approach represents the net cash flow with consideration of the time value of money, whereas cash payback technique neglects cash flows occurring after the payback period, and it does not use the present value concept (time value of money) in valuing cash flows that are occurring in the different time period. In other word, payback period approach measures the risk of the investment rather than the profitability.

If an investor is very concerned about the risk of an investment, the payback period approach is best for the decision making. Under this circumstance, opportunity 2 is better for the investment.

If an investor is very concerned about the profitability of an investment, the net present value approach is best for the decision making. Under this circumstance, opportunity 1 is better for the investment.