Question

The Taylor Corporation is using a machine that originally cost $66,000. The machine has a book value of $66,000 and a current market value of $40,000. The asset is in the Class 8 CCA pool. It will have no salvage value after 5 years and the company tax rate is 40%.
Jacqueline Elliott, the Chief Financial Officer of Taylor, is considering replacing this machine with a newer model costing $70,000. The new machine will cut operating costs by $10,000 each year for the next five years. Taylor's cost of capital is 8%.

Should the firm replace the asset? (Use NPV methodology to solve this problem.)

Calculate the Present Values of the followings:

1. Total cashflows in year 0:

($30,000)

($70,000)

($40,000)

$30,000

2. Total Annual Savings for the five years:

$23,956

$25,789

$45,378

$11,289

3. PV CCA:

$8,229

$7,963

$9,365

$10,345

How to do question 2 and 3?

Answer 1

Part 2)

The present value of annual savings is calculated with the use of formula given below:

Annual Savings = Decrease in Operating Costs*(1-Tax Rate) = 10,000*(1-40%) = $6,000

Present Value of Annual Savings = Annual Savings Year 1/(1+Cost of Capital)^1 + Annual Savings Year 2/(1+Cost of Capital)^2 + Annual Savings Year 3/(1+Cost of Capital)^3 + Annual Savings Year 4/(1+Cost of Capital)^4 + Annual Savings Year 5/(1+Cost of Capital)^5

Substituting values in the above formula, we get,

Present Value of Annual Savings = 6,000/(1+8%)^1 + 6,000/(1+8%)^2 + 6,000/(1+8%)^3 + 6,000/(1+8%)^4 + 6,000/(1+8%)^5 = $23,956.26 or $23,956 (which is Option A)

_____

Part 3)

The PV(CCA) is arrived as follows:

PV(CCA) = (Cost of New Machine - Salvage Value or Market Value of Old Equipment)*((CCA Rate*Tax Rate)/(Cost of Capital+CCA Rate))*((1+.5*Cost of Capital)/(1+Cost of Capital))

Substituting values in the above formula, we get,

PV(CCA) = (70,000-40,000)*[(20%*40%)/(8%+20%)]*((1+.5*8%)/(1+8%)) = $8,253.96 which is closest to $8,229 (which is Option A) [the slight difference in answer is on account of rounding off values]

_____

The NPV is calculated as below:

NPV = PV of Cash Flow in Year 0 + Present Value of Annual Savings + PV(CCA) = (-70,000 + 40,000) + 23,956 + 8,229= $2,185

The firm should replace the asset as it results in a positive NPV of $2,185.