Question

Factor Company is planning to add a new product to its line. To manufacture this product, the company needs to buy a new machine at a $515,000 cost with an expected four-year life and a $15,000 salvage value. All sales are for cash, and all costs are out-of-pocket, except for depreciation on the new machine. Additional information includes the following. (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

Expected annual sales of new product	$	1,950,000
Expected annual costs of new product
Direct materials		460,000
Direct labor		678,000
Overhead (excluding straight-line depreciation on new machine)		337,000
Selling and administrative expenses		158,000
Income taxes		38	%

Required:
1. Compute straight-line depreciation for each year of this new machine’s life.
2. Determine expected net income and net cash flow for each year of this machine’s life.
3. Compute this machine’s payback period, assuming that cash flows occur evenly throughout each year.
4. Compute this machine’s accounting rate of return, assuming that income is earned evenly throughout each year.
5. Compute the net present value for this machine using a discount rate of 7% and assuming that cash flows occur at each year-end. (Hint: Salvage value is a cash inflow at the end of the asset’s life.)

Answer 1

1. Calculation of depreciation (straight line method)

formula:

(cost of the machine - salvage value ) / life of the machine

= ($ 515,000 - $ 15,000) / 4

= $ 125,000

Therefore the depreciation of the new machine is $ 125,000 each year

2.

Calculation of expected net income:

particulars	amount ($)
Sales revenue	1950,000
less: direct materials	460,000
less:direct labor	678,000
less: overheads(excluding depreciation)	337,000
less: selling and distribution	158,000
less: depreciation	125,000
net operating income before tax	192,000
income tax (38%)	72,960
net operating income after tax	119,040

Calculation of expected net cash flow each year:

Particulars	Amount ($)
net operating income after tax	119,040
add: depreciation expense	125,000
expected net cash inflow each year	244,040

* As depreciation is a non cash expense it is added back to get net cash flow each year.

3. Calculation of machines payback period

in case where the cash flow occurs evenly throughout the year and the salvage value of the machine is given

formula:

(initial investment - salvage value) / annual cash flow from the asset

($ 515,000 - $ 15,000) / $ 244,040

= 2.04 years

working note:-

cost of machine ( initial investment) = $ 515,000

salvage value = $ 15,000

Annual cash inflow = 244,040

4. Calculation of the accounting rate of return of the machine:

As the cash flow occurs evenly throughout the year

formula:

accounting rate of return = average annual profit / average investment

= $ 119,040 / $ 265,000

= 0.4492

= 44.92%

explanation :

average investment = (opening value of initial investment + value of investment at the end of useful life) / 2

= ($ 515,000 + $ 15,000) / 2

= $ 265,000

average annual profit = total annual profit through out the useful life / useful life of the asset

= ($ 119,040 * 4) / 4

= $ 119,040

5.Calculation of the net present value of the machine

particulars	amount ($)
initial investment	(515,000)
Present value of annual cash inflows from year 1 to year 4 [ $ 244,040 * 3.3869]	826,539.07
salvage value at the end of year 4 [ $ 15,000 * 0.7628 ( refer working note) ]	11,442
Net present value	322,981.07

working note:-

Table showing present value discounting factors @ 7%

year	present value discounting factors @ 7%
1	0.9345
2	0.8734
3	0.8162
4	0.7628

The cumulative present value discounting factors for year 1 to 4 = 3.3869