Question

Two options to acquire a property priced at $350,000:

Option 1: Finance through the seller with 20%down and the balance due in 6 annual payments at 15%

Option2: Pay cash with 12% discount

What is the IRR for the loan offered by the seller?

Answer 1

In option 1 you are required to make a down payment of 20% that is $ 70,000 and on the remaining amount in 6 annual payments at a rate of 15%.

Annual payment can be calculated as follows

Therefore, you are required to make an annual payment of $ 73,986 for next 6 years.

Under second option you get a discount of 12% when you pay in cash.

You are required to pay = $ 350,000*(1-0.12) = $ 308,000

Now, for the seller the present worth of the annual payment,if discounted at IRR, that we pay under plan 1 must be equal to PW of plan 2.

we can determine the IRR using trial and error method. Assume rate = 10%

The NPW is not eqaul to zero. Since it is positive therefore assume a higher discount rate.

Assume rate = 11%

Again we have to increase the discount it. Assume rate = 12%

As we can see for 11% the NPW is greater than zero and at 12% it is less than zero hence the required value lies in between 11% to 12%. We can determine it using linear interpolation

Required IRR = 11.57%.

Solved it using excel too got 11.56%. Refer the attached screenshot