# Choosing between investing or buying now

1. Feb 19, 2014

### ainster31

1. The problem statement, all variables and given/known data

A group of students decided to lease and run a gasoline service station. The lease is for 10 years. Almost immediately the students were confronted with the need to alter the gasoline pumps to read in litres. The Dayton Company has a conversion kit available for $900 that may be expected to last 10 years. The ﬁrm also sells a$500 conversion kit that has a 5-year useful life. The students believe that any money not invested in the conversion kits may be invested elsewhere at a 10% interest rate. Income tax consequences are to be ignored in this problem.
(a) Assuming that future replacement kits cost the same as today, which alternative should be selected?
(b) If one assumes a 7% inﬂation rate, which alternative should be selected?

2. Relevant equations

3. The attempt at a solution

For part b, here is the solution:

(b) Replacement cost of $500 kit, five years hence =$500 (F/P, 7%, 5) = $701.5 PW$500 kit = $500 +$701.5 (P/F, 10%, 5) = $935.60 PW$900 kit = $900 To minimize PW of Cost, choose$900 kit.

So, the $500 was converted from 500 current-dollars to 701.50 5-year-future-dollars. Then, the 701.50 5-year-future-dollars was converted to$435.60 current dollars using the 10% interest for the investment but I think they forgot to account for the inflation rate. Instead of using 10%, shouldn't they have used the market rate?

Last edited: Feb 19, 2014
2. Feb 19, 2014

### ainster31

Ah, I get it now. The 10% interest includes the inflation rate because it is the market interest rate which is the combination of the real interest rate and inflation rate.