Question

This is a cost accounting problem, please show all work.

New equipment purchase, income taxes. Ella's Bakery plans to purchase a new oven for its store. The oven has an estimated useful life of 4 years. The estimated pretax cash flows for the oven are as shown in the table that follows, with no anticipated change in working capital. Ella's Bakery has a 14% after-tax required rate of return and a 35% income tax rate. Assume depreciation is calculated on a straight-line basis for tax purposes using the initial investment in the oven and its estimated terminal disposal value. Assume all cash flows occur at year-end except for initial investment amounts. Home Insert Page Layout Α. B F Formulas Data Review View C D E Relevant Cash Flows at End of Each Year 0 1 2 3 / ($186,000) 4 2 3 Initial oven investment |Annual cash flow from operations 4 l(excluding the depreciation effect) 5 Cash flow from terminal disposal of oven $77,000 $77,000 $77,000 $77,000 $ 6,000 Required: 1. Calculate (a) net present value, (b) payback period, and (c) internal rate of return. 2. Calculate accrual accounting rate of return based on net initial investment.

Answer 1

Solution

(1)

Annual Cash Inflow = $ 77000

Estimated Life = 4 Years

Initial Investment = $ 186000

Salvage Value = $ 6000

Depreciation (Straight Line Basis) = (Initial Investment - Salvage Value) / Estimated Life

=$[(186000-6000)/4]

=$ 45000

Tax Rate = 35%

Cash Flow after Depreciation = $ (77000-45000) = $ 32000

Tax = $ 32000 X 35% = $ 11200

Cash Flow After Tax (CFAT) = (Cash flow after depreciation - Tax + Depreciation)

= $ (32000 - 11200 + 45000)

= $ 65800

(a) Net Present Value:

Initial Outlay = $ 186000

CFAT = $ 65800

Salvage Value = $ 6000

Life (n) = 4 years

Rate of Return (r) = 14%, or 0.14

Present Value Interest Factor for 4 years @ 14% (PVIF_14,4) = 1/(1+r)^n

=1/[(1.14)^4] = 0.5921

Present Value Interest Factor of Annuity for 4 years @ 14% (PVIFA_14,4) = {1 - [1/(1+r)^n]} / r

= {1-[1/(1.14)^4]} / 0.14

= 2.9137

Discounted CFAT = $ (65800 X 2.9137) = $ 191,721.46

Present Value of Salvage = $ (6000 X 0.5921) = $ 3,552.60

Net Present Value = Discounted CFAT + PV of Salvage - Initial Outlay

= $ (191721.46 + 3552.60 - 186000)

= $ 9274.06

Therefore, Net Present Value = $ 9274.06

(b) Payback Period = Initial Investment / CFAT

= 186000 / 65800

= 2.83 (Approx)

Therefore, Payback Period is 2.83 Years

(c) Internal Rate of Return:

Refer to following table,

Year	CFAT ($)	PVIF @ 16%	Disc. CFAT ($)	PVIF @ 17%	Disc. CFAT ($)
1	65,800.00	0.8621	56,724.14	0.8547	56,239.32
2	65,800.00	0.7432	48,900.12	0.7305	48,067.79
3	65,800.00	0.6407	42,155.27	0.6244	41,083.58
4	65,800.00	0.5523	36,340.75	0.5337	35,114.17
4 (Salvage)	6,000.00	0.5523	3,313.75	0.5337	3,201.90
Total Inflow			1,87,434.03		1,83,706.76

At IRR, Total Inflow = Initial Outflow

Here, At 16%, Inflow = $ 187434.03

and, At 17%, Inflow = $ 183706.76

So, assuming at X% Inflow will be $ 186000, value of X using Interpolation

(X - 16) / (17 - 16) = (186000 - 187434.03) / (183706.76 - 187434.03)

Or, X - 16 = 1434.03 / 3727.27

Or, X - 16 = 0.385 (Approx)

Or, X = 16.39 (Approx)

Therefore, Internal Rate of Return = 16.39%

(2)

For Computing Acoounting Rate of Return,

Average Net Profit = $ (32000 - 11200) [ As uniform cash flow throughout the project span]

= $ 20800

Average Investment = (Initial Investment + Salvage Value) / 2

= $ (186000+6000)/2

= $ 96000

Accounting Rate Of Return = (Average Net Profit / Average Investment) x 100

= (20800/96000)X100

= 21.67 % (Approx)

Therefore, Accounting Rate of Return is 21.67%