Question

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Problem 5-34 Annuity Due (L03) Your landscaping company can lease a truck for $8,800 a year (paid at year-end) for 5 years. It can instead buy the truck for $38.000 The truck will be valueless after 5 years. The interest rate your company can earn on its funds is 6%. a. What is the present value of the cost of leasing? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Present value of lease b. Is it cheaper to buy or lease? Buy Lease c. What is the present value of the cost of leasing if the lease payments are an annuity due, so the first payment comes immediately? (Do not round Intermediate calculations. Round your answer to 2 decimal places.) Present value of

Answer 1

a.

The present value of lease payments payable at the end of period can be calculated with the help of below expression:

1-(1+i) Present value = Annual amount Here, i is interest rate, nis number of years.

Substitute $8,800 for annual amount, 0.06 for i, and 5 for n,

(1-(1+0.06) Present value = $8,800 x 0.06 = $8,800x( 0.252741 ) W 0.06 = $8,800x 4.21236 = $37,068.80

b.

From the two alternative option, individual should choose for lease payments on truck. This is because the present value of lease payments is lower than today purchase price of the truck. Hence, it is cheaper.

c.

The present value of lease payments payable annually starting immediately can be calculated with the help of below expression:

Present value = Annual amount 1-(1+i) - ) (1-(1+i) Here, i is interest rate, nis number of years.

The present value is calculated below:

1-(1 Present value = $8,800 x (1-(1+0.06)") (0.252741) = $8,800 x 0.0566) = $8,800 x 4.4651 = $39,292.92

d.

If lease payments started immediately, then present value of such payments will be $39,292.92 which is higher than the purchase price of truck. Thus, it is advisable to buy the truck for $38,000 which will be cheaper for the individual.

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