Question

ABC plc has a new product ready for production and sale. Fixed costs of production (excluding depreciation) are expected to be £200,000 a year. This figure is made up of £160,000 additional fixed costs and £40,000 fixed costs relating to the existing business which will be apportioned to the new product. The company estimates that the product will sell 150,000 units a year over the next five years. The sale price will be £5 per unit and variable costs are estimated to be £3 per unit.

In order to produce the product, machinery priced at £520,000 is needed and immediately payable. The estimated salvage value of this machinery in five years’ time is £100,000. The business calculates depreciation on a straight-line basis. ABC plc has invested £200,000 to date in researching on the new product, and borrowed the research cost at a cost of 7 percent per annum. The machinery cost will be borrowed at a cost of 8 percent per annum.

The business has a cost of capital of 12 per cent. Ignore taxation.

a.          Calculate the net present value of the product, with explanation on the working.

b.         Undertake sensitivity analysis to show by how much the following factors would have to change before the product ceased to be worthwhile:

i.             The discount rate.

            Use the method of interpolation with r values of 12% and 20%.                     

ii.            The initial outlay on machinery.   .           

iii.           The residual value of the machinery.

Answer 1

The answer to the following parts:

a. (i) Annual Cash Flow

Sales per unit $ 5

Variable cost per unit $3

Contribution per unit $ 2

Total Contribution $2 * 150000 units

=$ 300000

Less Fixed Costs =$ 200000

Less Depreciation

($520000+ Interest borrowed $ 208000)= $728000

R& D cost

($ 200000+ interest borrowed $ 70000) =$270000

Total =$998000

Salvage value =$100000

No of years =5

Depreciation on straight line basis =$998000-$100000/5

=$179600

EBT =($ 79600)

+ Depreciation =$179600

Annual Cash inf low =$100000

NPV

PV of cash inflows ($100000 * PV of 10% for 5 years ie 3.7906) =$379600

PV of cash outflow ($520000+ $200000) =$720000

NPV =($340940)

b i = PV of cash inflows @ 12% for 5 years =$ 100000* 3.6045=$360450

PV of cash inf lows @ 20% for 5 years =$ 100000* 2.9904 =$299040

IRR = 12 + ($360450 -$720000)/($360450-$299040)*(20-12)

= 12 -46.8 =(34.8) which is a -Ve sensitivity as the NPV is also negative.

ii. let the investement =X

-X +$100000* 3.7906 ie pv of 10% for 5 years =0

or X =$ 397600

so the investment should decrease by $ 720000-$297600 =$322400 in order to make the NPV equal to zero ie to break even with no profit or loss.

iii. Let the life be X years

-$720000 +$100000 A_{x 0.10^{= 0}}

A_{x .10^{= $720000/$100000}}

_^=7.2

A_7*.10 =4.868

A_8*.10 =5.334

By simple interpolation

7+ (4.868-3.7906)/(5.334-4.868)*1

=9.30 years

so if the life of the asset decrease by 2.30 years the NPV will be positive.