Question

A construction company is choosing between two backhoes. Options A is a wheel-mounted version, with an initial cost of $65,000, an expected life of 6 years, and a salvage value of $5,000. Option B is a trackmounted version, with an initial cost of $85,000, a 9-year life, and a salvage value of $10,000. Both machines will achieve the same productivity. The interest rate is 9%.

a) What is the EUAC of option A ($/year)?

b) What is the EUAC of option B ($/year)?

c) If the interest rate is 12%, which option is preferred (A or B)?

Answer 1

The life of both the options is different. We have to convert the unequal life into equal life by using the common multiple method. The LCM of 6 years and 9 years is 18 years. So the Option A is repeated 3 times and the Option B is repeated 2 times.

a) What is the EUAC of option A ($/year)?

Initial Cost = 65,000

Salvage Value = 5,000

Interest rate = 9%

Step – 1 Calculate the PW

PW = 65,000 + 65,000 (P/F, 9%, 6) + 65,000 (P/F, 9%, 12) - 5,000 (P/F, 9%, 6) - 5,000 (P/F, 9%, 12) - 5,000 (P/F, 9%, 18)

PW = 65,000 + 65,000 (0.5963) + 65,000 (0.3555) - 5,000 (0.5963) - 5,000 (0.3555) - 5,000 (0.2120)

PW = 121,048

Step – 2

EUAC = PW (A/P, 9%, 18)

EUAC = 121,048 (0.1142)

EUAC = 13,824

b) What is the EUAC of option B ($/year)?

Initial Cost = 85,000

Salvage Value = 10,000

Interest rate = 9%

Step – 1 Calculate the PW

PW = 85,000 + 85,000 (P/F, 9%, 9) – 10,000 (P/F, 9%, 9) – 10,000 (P/F, 9%, 18)

PW = 85,000 + 85,000 (0.4604) – 10,000 (0.4604) – 10,000 (0.2120) = 117,410

Step – 2

EUAC = PW (A/P, 9%, 18)

EUAC = 117,410 (0.1142)

EUAC = 13,408

At interest rate 9%, EUAC of Option A = 13,824

                                      Option B = 13,408

Select the Option B.

c) If the interest rate is 12%, which option is preferred (A or B)?

What is the EUAC of option A ($/year)?

Initial Cost = 65,000

Salvage Value = 5,000

Interest rate = 12%

Step – 1 Calculate the PW

PW = 65,000 + 65,000 (P/F, 12%, 6) + 65,000 (P/F, 12%, 12) - 5,000 (P/F, 12%, 6) - 5,000 (P/F, 12%, 12) - 5,000 (P/F, 12%, 18)

PW = 65,000 + 65,000 (0.5066) + 65,000 (0.2567) - 5,000 (0.5066) - 5,000 (0.2567) - 5,000 (0.1300)

PW = 110,148

Step – 2

EUAC = PW (A/P, 12%, 18)

EUAC = 110,148 (0.1379) = 15,189

What is the EUAC of option B ($/year)?

Initial Cost = 85,000

Salvage Value = 10,000

Interest rate = 12%

Step – 1 Calculate the PW

PW = 85,000 + 85,000 (P/F, 12%, 9) – 10,000 (P/F, 12%, 9) – 10,000 (P/F, 12%, 18)

PW = 85,000 + 85,000 (0.3606) – 10,000 (0.3606) – 10,000 (0.1300) =

Step – 2

EUAC = PW (A/P, 12%, 18)

EUAC = 110,745 (0.1379) = 15,272

At interest rate 12%, EUAC of Option A = 15,189

                                      Option B = 15,272

Select the Option A.