Question

A company manufactures product X which it sells for $5 per unit. Variable costs of production are currently $3 per unit. A new machine is available which would cost $90,000 but which could be used to make product X for a variable cost of only $2.50 per unit. However, when the company decides to invest in this new machine, it would increase its fixed costs by $7,500 a year as a direct result of purchasing the machine. The machine would have an expected life of four years and a resale value after that time of $10,000. Sales of product X are estimated to be 75,000 units a year.

i.    If the company expects to earn at least 12 % a year from its investments, should the machine be purchased? (Ignore taxation).

ii.   Without doing any calculation, what will be the expected rate of return from an investment in this new machine?

Answer 1

i. We need to find the net present value (NPV) of all the incremental cash flows associated with the purchase

NPV= Initial cost of the machine+PV of 4 yrs.' incremental contribution-PV of increased annual fixed costs+PV of salvage at end yr.4

ie.NPV=-90000+(75000*((5-2.50)-(5-3))*3.03735)-(7500*3.03735)+(10000*0.63552)

ie. -90000+113900.63-22780.13+6355.20=

7475.70

NOTE: P/A Factor , for i=12% & n=4----3.03735 & PV /F for i=12% & yr.4= 0.63552

YES.

Bettys and Co. should purchase the machine

as the NPV of the relevant cash flows discounted at the expected rate of return of 12% is POSITIVE ($ 7475.70) which will add value to the firm & its owners.

ii. Expected rate of return is 12% (as given in ques. 1 )