Question

Drake Corporation is reviewing an investment proposal. The initial cost and 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 schedule below. 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 equal to its book value. There would be no salvage value at the end of the investment’s life.

Investment Proposal
Year		Initial Cost and Book Value			Annual Cash Flows			Annual Net Income
0		$104,000
1		70,900			$46,000			$12,900
2		42,500			40,600			12,200
3		20,400			35,900			13,800
4		8,600			30,100			18,300
5		0			25,000			16,400

Drake Corporation uses an 11% target rate of return for new investment proposals.

Click here to view PV table.

(a)

What is the cash payback period for this proposal? (Round answer to 2 decimal places, e.g. 10.50.)

Cash payback period

years

(b)

What is the annual rate of return for the investment? (Round answer to 2 decimal places, e.g. 10.50.)

Annual rate of return for the investment

%

(c)

What is the net present value of the investment? (If the net present value is negative, use either a negative sign preceding the number eg -45 or parentheses eg (45). Round answer to 0 decimal places, e.g. 125. For calculation purposes, use 5 decimal places as displayed in the factor table provided.)

Net present value

$

Answer 1

1. Cash pay back period

Year	cash flow for the period	cumulative cash flow
0	$ (104,000)	$ (104,000)
1	$ 46,000	$ (58,000)
2	$ 40,600	$ (17,400)
3	$ 35,900	$ 18,500
4	$ 30,100	$ 48,600
5	$ 25,000	$ 73,600

Payback period = Initial Investment / cash flow for the period

When cash flow the period are uneven, cumulative cash flow is to be taken

Payback period = A + ( B/C)

Where,

A is the last period number with a negative cumulative cash flow;

B is the absolute value (i.e. value without negative sign) of cumulative net cash flow at the end of the period A; and

C is the total cash inflow during the period following period A

Payback period = 2 year + (17,400/35,900)

= 2.48 years

2. Annual rate of return

= Average annual profit / Initial Investment

=$ { (12, 900+12,200+13,800+18,300+16,400)/5} / $104,000

=$ 14,720 / $ 104,000

= 14.15 %

3. Net Present value

Year	cash flow	computation	Present Value
0	$ (104,000)	-	$ (104,000)
1	$ 46,000	$46,000/(1.11)	$41,441.441
2	$ 40600	$40,600/(1.11)^²	$32,951.871
3	$ 35,900	$35,900/(1.11)^³	$26,249.771
4	$ 30,100	$30,100/ (1.11)^⁴	$19,827.802
5	$ 25,000	$25,000/(1.11)^5	$14,836.283
	Total		$31,307.168

Net present value = $ 31,307.168