Eat at State is considering buying a new food truck. It will cost $65,000, but is expected to generate $20,000 in sales each year over the next 4 years. At the end of the 4th year, the truck will be sold to Eat Like a Wolverine in Ann Arbor for $10,000 (after taxes). It will require $5,000 in additional Net Working capital that will not be recovered when the truck is sold. The Dean of Food Services will only authorize the purchase if it is cash positive by the end of the 4th year. Using the payback period method, should the truck be purchased, and why?

The Present Worth of the machine if the real interest rate is 10% per year and the inflation rate is 5% per year, using:

(a) constant-value dollars

= $10,518.60

(b) then-current dollars

= $10,818.65

Explanation:

a) Data and Calculations:

Cost a certain machine six years from now = $25,000

Time period = 6 years

Real interest rate = 10%

Inflation rate = 5%

Nominal interest rate = 5% (10% - 5%)

Discount factor at 10% for 6 years = 0.564

Discount factor at 5% for 6 years = 0.746

PW using:

a) Constant-value dollars = $18,650 ($25,000 * 0.746)

PW = $10,518.60 ($18,650 * 0.564)

b) Then-current dollars:

The nominal rate = 0.1 + 0.05 + (0.1 * 0.05) = 0.155

$10,818.65 ($25,000 * 0.432746)