Question

A machine is purchased by making payments of $16,000 at the beginning of each of five years with the first payment to be made today. Company determines the cost of the machine is $65,000. What was the implicit interest rate? (Use Time factor table)

Time Factors

Present Value of Ordinary Annuity

Periods 5

9% = 3.88965

10% = 3.79079

11% = 3.69590

12% = 3.60478

Answer 1

According to question, a machine is purchased by making payments of $ 16,000 at the beginning of each of 5 Years. Cost of Machine is $ 65,000.

Required: - Calculate Implicit Interest Rate or Internal rate of return (IRR)

At Implicit interest rate, Present Value of cash inflow = Present Value of cash outflow

Implicit Interest Rate is the interest rate where,

PVAF (Interest rate, 5) x $ 16,000 = $ 65,000

[PVAF = Present value annuity factor]

1. Say at interest rate of 9% we get,

PVAF (9%, 5) x $ 16,000= 3.88965 x $ 16,000 = $ 62,234.40

2. Again say at interest rate of 11% we get,

PVAF (11%, 5) x $ 16,000= 3.69590 x $ 16,000= $ 59,134.40

Therefore using interpolation we find interest rate where, PVAF (Interest rate, 5) = $65,000

Let the desired implicit interest rate be A

Therefore,

A - 9	=	65000 - 62234.4
11 - 9		59134.4 - 62234.4

So, A = 7.22 %              

The desired implicit interest rate is 7.22%