Question

An asset can be purchased today at an installed cost of $1,000. It is forecast to generate annual operating net cash inflows of $250 for the next five years and to be sold for $100 at the end of four years. (Assume that there is no income tax and that annual net cash flows occur at the end of each year.)

(a)     Draw a time-line showing all the cash flows relating to this asset.                   (1 mark)

(b)     Using a discount rate of 10% per year, what is the present value of the forecast cash inflows? (Give your answer to the nearest cent.)                                                                             

         

(c)     Using the present value you calculated in part (b), what is the net present value of this project? (Give your answer to the nearest cent.)                                                                       (1 mark)

           

(d)     If the asset is depreciated at the rate of $200 per year:

          (i)      What will be the accounting profit in years 1 to 4?                                 (1 mark)

                  

          (ii)     What will be the accounting profit in year 5?                                          (1 mark)

                  

          (iii)    What will be the average annual accounting profit?                                (1 mark)

                  

          (iv)    What will be the average investment (based on the asset’s installed cost and salvage value)?   (1 mark)

                  

            (v)        What will be the accounting rate of return? (Give your answer in percentage points to two decimal places.)

Answer 1

a
Years
0__________1__________2__________3__________4__________5
-$1000 $250 $250 $250 $350 $250
Cash Flows
b
Present value of the future cash inflows:
Year	Cash Flow	Discount factor @ 10%*	Present Value
1	250	0.9091	227.27
2	250	0.8264	206.61
3	250	0.7513	187.83
4	350	0.683	239.05
5	250	0.6209	155.23
		TOTAL	1016
Present Value of future inflows = $ 1016
* Discount factor is calculated as follows:
Year 1 = 1/1.101 = 0.9091
Year 2 = 1/1.102 = 0.8264
and so on.
c
Net Present value = Present Value of Inflows - Present Value of Outflows = 1016 - 1000 = $ 16
d
i.
	Year 1	Year 2	Year 3	Year 4
Cash Inflows	250	250	250	250
Depreciation	-200	-200	-200	-200
Loss on sale of asset*				-100
Accounting profit	50	50	50	-50
Loss on sale of asset is calculated as follows:
Cost of asset = $ 1000
Depreciation for 4 years = 200 *4 = $ 800
Book value at end of 4 years = $ 200
Sales Amount = $ 100
Hence, loss = 100 - 200 = $ 100
ii.
Accounting profit in year 5:
As there is no depreciation expense, Cash Inflow = Accounting profit = $ 250
iii.
Average annual profit = Sum of profits for 5 years / 5 = 350 / 5 = $ 70
iv
Average Investment = (Installed Amount - Salvage Amount) / 5 = (1000 - 100) / 5 = $ 180
v
Accounting rate of return = Average annual accounting profit / Average investment
= 70 / 180 (Both calculated above)
0.3889