Answer to Question #131049 in Finance for Tila Masinge

Question

This co. is required to replace its trucks regularly owing to the importance of providing a reliable service to customers. The company is considering investing in a new truck at a cost of K1.2 million. Finozest’s bank has indicated that it can offer the company a finance lease with payments of K292,510.00, payable annually in arrears for five years. There is no residual payment or value. Kindly ignore taxation.

1. What is the interest rate implicit in the finance lease?

2. Assume that the bank wishes to keep the lease payment at K292,510.00 but requires that the annual payments are payable in advance. How does this change the interest rate implicit in the lease?

3. Assume that the truck has an expected residual value of K450,000 at the end of five years and the bank takes this residual value into account in setting the lease payments, which are payable annually in advance. How would this change your lease payment?

Answer 1

solution 1

Let PV be the present value of the loan amount, P be the annual payments r be the interest rate and n the number of payments.

$P=292,510$

$n = 5$

$$PV = P * \frac{1-(1+r)^{-n}}{r}$$

With no residual value,

$PV = 1,200,000$

Therefore;

$$1,200,000 = 292,510 * \frac{1-(1+r)^{-5}}{r}$$

$$4.1024 = \frac{1-(1+r)^{-5}}{r}$$

Using the Excel formula;

Rate (nper, pmt, PV, type=0)

interest rate charged on the loan is 6.98%

Answer: 6.98%

solution 2

when payments are made in advance, the present value is obtained as;

$$PV = P + P * \frac{1-(1+r)^{-(n-1)}}{r}$$

$$1,200,000 = 292,510 + 292,510* \frac{1-(1+r)^{-4}}{r}$$

$$907,490 = 292,510 * \frac{1-(1+r)^{-4}}{r}$$

$$3.1024 = \frac{1-(1+r)^{-4}}{r}$$

Using the Excel formula;

Rate (nper, pmt, PV, type=0)

interest rate charged on the loan is 11.00%

Answer: 11.00%

solution 3

When lease payments are made annually in advance;

$$PV = P + P * \frac{1-(1+r)^{-(n-1)}}{r}$$

Residual value at the end of 5 years is K 450,000.

Present value of the residual value is

$$PV=\frac{amount}{(1+r)^n}$$

$$PV=\frac{450,000}{(1+0.11)^5} = 267,053.1$$

Deduct the present value of the residual value from the present value, we have:

$$PV = 1,200,000-267053.1= 932,946.90$$

At the annual interest rate of 11.00%, the annual payments will be:

$$932,946.90= P + P * \frac{1-(1+0.11)^{-4}}{0.11}$$

$$932,946.90 = P + 3.102446 P$$

$$P = \frac{932,946.90}{1+3.102446} = 227,412.40$$

annual lease payments when residual value is considered is K 227,412.40

answer: annual lease payments fall from K 292,510.00 to K 227,412.40