Question

Cybertrex, a manufacturing facility, rented a new piece of equipment on January 1st and agreed to pay an annual rental fee of $18,000 at the end of each of the next 10 years. The weighted average cost of capital of the company is 8%. The present value of $1 for 10 years at 8% is 0.46319 The present value of an ordinary annuity of $1 for 10 years at 8% is 6.71008 What is the Present Value of the rental payments over 10 years?
1) $180,000
2) $55,945
3) $8,337
4) $120,781

Answer 1

Answer:

4) $120,781

Explanation:

You can calculate the present value of the rental payments in two different ways:

1) multiply the value of the annuity times the present value of the annuity for 10 years = $18,000 x 6.71008 = $120,781

2) or you can divide calculate the present value of every annuity and then add them up

present value = ($18,000 / 1.08) + ($18,000 / 1.08²) + ($18,000 / 1.08³) + ($18,000 / 1.08⁴) + ($18,000 / 1.08⁵) + ($18,000 / 1.08⁶) + ($18,000 / 1.08⁷) + ($18,000 / 1.08⁸) + ($18,000 / 1.08⁹) + ($18,000 / 1.08¹⁰) = $16,667 + $15,432 + $14,289 + $13,321 + $12,250 + $11,343 + $10,503 + $9,723 + $9,004 + $8,337 = $120,781