Question

Blossom Corporation is reviewing an investment proposal. The initial cost is $105,700. Estimates of the book value of the investment at the end of each year, the net cash flows for each year, and the net income for each year are presented in the following schedule. All cash flows are assumed to take place at the end of the year. The salvage value of the investment at the end of each year is assumed to equal its book value. There would be no salvage value at the end of the investment’s life. Investment Proposal Year Book Value Annual Cash Flows Annual Net Income

1 $70,500 $44,900 $9,700
2 42,400 39,200 11,100
3 20,600 36,000 14,200
4 6,800 29,100 15,300
5 0 25,205 18,405
Blossom Corporation uses an 11% target rate of return for new investment proposals.
(a)

What is the cash payback period for this proposal?

(b)

What is the annual rate of return for the investment?

(c)

What is the net present value of the investment?

Answer 1

**(a) Cash Payback Period:**
The cash payback period is the time it takes for the initial investment to be recovered through net cash flows. To calculate it, you sum the net cash flows until they cover the initial cost.

| Year | Net Cash Flow |
|------|---------------|
| 1 | $44,900 |
| 2 | $39,200 |
| 3 | $36,000 |
| 4 | $29,100 |
| 5 | $25,205 |

The cumulative net cash flow at the end of Year 4 is $44,900 + $39,200 + $36,000 + $29,100 = $149,200. The cash payback period falls within Year 4, and the remaining amount to recover in Year 5 is $105,700 - $149,200 = -$43,500.

Therefore, the cash payback period is approximately 4 years, with partial recovery in Year 5.

**(b) Annual Rate of Return:**
The annual rate of return (ARR) is calculated using the average annual accounting profit divided by the initial investment.

\[ARR = \frac{\text{Average Annual Net Income}}{\text{Initial Investment}}\]

Average Annual Net Income = \(\frac{\$9,700 + \$11,100 + \$14,200 + \$15,300 + \$18,405}{5} = \$13,541\)

\[ARR = \frac{\$13,541}{\$105,700} \times 100\]

The annual rate of return is approximately 12.81%.

**(c) Net Present Value (NPV):**
The Net Present Value is calculated by subtracting the initial investment from the present value of the expected cash inflows.

\[NPV = \sum_{t=1}^{5} \frac{\text{Net Cash Flow}_t}{(1 + \text{Discount Rate})^t} - \text{Initial Investment}\]

Given the 11% target rate of return:

\[NPV = \frac{\$44,900}{(1 + 0.11)^1} + \frac{\$39,200}{(1 + 0.11)^2} + \frac{\$36,000}{(1 + 0.11)^3} + \frac{\$29,100}{(1 + 0.11)^4} + \frac{\$25,205}{(1 + 0.11)^5} - \$105,700\]

The NPV is approximately $9,594.34.