Question

E23-9 Mimulus Inc. is considering a capital investm Calculate annual rate of machinery is expected to have a useful life of five years with sidering a capital investment of $300,000 in additional productive facilities. The new method. During the life of the investment, annual profit and cas have a useful life of five years with no residual value. Depreciation is by the straight-line return, cash payback period, respectively. Mimulus has a 15% cost of capital rate, which is the minimum une investment, annual profit and cash inflows are expected to be $30,000 and $90,000, and net present value. (LO 3, 4) AP S has a 15% cost of capital rate, which is the minimum acceptable rate of return on the investment Instructions (Round to two decimals.) (a) Calculate: (1) the annual rate of return, and (2) the cash payback period on the proposed capital expenditure, (b) Using the discounted cash flow technique, calculate the net present value.

When I did a search for this question, the steps and answers given are different from my calculations below. Can someone please help with a step by step? Thank you!

Answer 1

Solution

Initial Investment = $ 300,000

Life = 5 Years

Residual Value = NIL

Therefore, Depreciation per year = $ (300,000/5) = $ 60,000

Annual Profit = $ 30,000

Cash Inflow After Tax (CFAT) = $ 90,000 (Which is also proved by adding the Annual Depreciation and Annual Profit)

(a)

(1) Annual Rate of Return = (Annual Profit / Initial Investment) X 100

= (30000 / 300000) X 100

= 10%

(b) Cash Payback Period:

Year	CFAT	Cumulative CFAT
	($)	($)
1	90,000.00	90,000.00
2	90,000.00	1,80,000.00
3	90,000.00	2,70,000.00
4	90,000.00	3,60,000.00
5	90,000.00	4,50,000.00

Cash Payback Period shows that within how much time frame our Initial Outlay will be recovered, without considering the Time Value of Money.

As per the given table, it can be seen that Initial Investment of $ 300,000 will be recovered in 3 to 4 Years as the Cumulative CFAT ranges $ 270,000 - $ 360,000.

So, assuming at X year Cumulative CFAT = $ 300,000, Value of X using Interpolation,

(X-3)/(4-3) = (300000-270000)/(360000-270000)

Or, X-3 = 30000/90000

Or, X-3 = 0.333 (Approx)

Or, X = 3+0.333

Or, X = 3.33 (Approx)

Therefore, The Cash Payback Period should be 3.33 Years.

(2)

Year	CFAT	PVIF @ 15%	Discounted CFAT ($)
(n)	($)	[1/(1+r)n]	(CFAT * PVIF)
1	90,000.00	0.8696	78,260.87
2	90,000.00	0.7561	68,052.93
3	90,000.00	0.6575	59,176.46
4	90,000.00	0.5718	51,457.79
5	90,000.00	0.4972	44,745.91
Total Discounted CFAT			3,01,693.96
Less: Initial Outlay			-3,00,000.00
NET PRESENT VALUE			1,693.96

Therefore, Net Present Value = $ 1,693.96