Question

Dr. Ryan wants to calculate the scrap value of a grill 20 years after purchase. According to him, using the declining-balance method, better represents depreciation. However he does not know what figure to use for depreciation rate. She goes on craigslist, and observes that a grill that was purchased for $245,000 three years ago, has a current salvage value of $180,000. What is a good estimate of the value of her grill after 20 years, if she buys one for $260,000 today?

Answer 1

A good estimate of the value of her grill after 20 years = $33,254

Explanation:

Let DB Depreciation rate be R%. Then

Salvage value in 1st year after purchase ($) = 245,000 x (1 - R)

Salvage value in 2nd year after purchase ($) = 245,000 x (1 - R)2

Salvage value in 3rd year after purchase ($) = 245,000 x (1 - R)3

Therefore,

245,000 x (1 - R)3 = 180,000

(1 - R)3 = 0.7347

Taking cube root,

1 - R = 0.9023

Therefore,

Value after 20 years ($) = 260,000 x (1 - R)20 = 260,000 x (0.9023)20 = 260,000 x 0.1279 = $33,254