Question

Paisley Motors helped out a vendor by lending them money to upgrade their supply chain. Paisley is willing to give the vendor some time before repaying the loan. The vendor will start making payments of $27,737 at the end of year 10, decreasing the payment amount by 22% each subsequent year. The vendor will make a total of 8 payments (one at the end of each year).

The company is thinking of selling the loan to a third party and needs to know how much the future loan payments are worth today. Use a nominal annual interest rate of 5%, compounded monthly to make the calculation.

Answer 1

Effective interest rate = (1+0.05 / 12)^12 -1

= 1.051161898 -1

= 0.051161898 ~ 0.0512

Present value at EOY 9 = 27737 * [1-(1-0.22)^8 / (1+0.0512)^8] / (0.0512 + 0.22)

= 27737 * [1- 0.78^8 / (1.0512)^8] / 0.2712

= 27737 * 3.3484837

= 92876.89

Present value at EOY 0 = 92876.89 / (1+0.0512)^9

=  92876.89 / (1.0512)^9

= 59256.98 ~ 59257 (Nearest Dollar)