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Financial Management (FINE 3010) Spring 2014

Practice 8 - 10

Equivalent Annual Annuity Problem 8.28

A firm can lease a truck for 4 years at a cost of $30,000 annually. It can instead buy a truck at a cost of

$80,000, with annual maintenance expenses of $10,000. The truck will be sold at the end of 4 years for

$20,000. Which is the better option if the discount rate is 10%?

Solution

Buy. PV of costs = $80,000 + [$10,000 annuity factor (10%, 4 years)] [$20,000/(1.10)4]

= $80,000 + $31,698.65 $13,660.27 = $98,038.38

The equivalent annual cost is the payment with the same present value. Solve the following equation for C:

[C annuity factor (10%, 4 years)] = $98,038.38 => C= EAC = $30,928.25

Using a financial calculator, enter n = 4; i = 10; FV = 0; PV = ()98,038.38; compute PMT ($30,928.25).

Financial Management (FINE 3010) - FA 2014 Practice 8 - 10

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Equivalent Annual Annuity Problem 8.28

A firm can lease a truck for 4 years at a cost of $30,000 annually. It can instead buy a truck at a cost of

$80,000, with annual maintenance expenses of $10,000. The truck will be sold at the end of 4 years for

$20,000. Which is the better option if the discount rate is 10%?

Solution

If you can lease instead for $30,000, then this is the less costly option.

You can also compare the PV of the lease costs to the total PV of buying:

$30,000 annuity factor (10%, 4 years) = $95,095.96

The PV of the lease costs is less than the PV of the costs when buying the truck.


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Solution

Project Evaluation


Find the equivalent annual cost of each alternative:

Blooper Industries must replace its magnoosium purification system. Quick & Dirty Systems sells a relatively cheap purification system for $10 million. The system will last 5 years. Do-It-Right sells a sturdier but more expensive system for $12 million; it will last for 8 years. Both systems entail $1 million in operating costs; both will be depreciated straight-line to a final value of zero over their useful lives; neither will have any salvage value at the end of its life. The firm's tax rate is 35%, and the discount rate is 12%. Which system should Blooper install? (Hint: Check the discussion of equivalent annual annuities in the previous chapter.)

Problem 9.24 4

Quick and Dirty Do-It-Right

Operating costs $1 million $1 million

Investment $10 million $12 million

Project life 5 years 8 years

Annual depreciation $2 million $1.5 million

Depreciation tax shield $0.700 million $0.525 million

PV(depreciation tax shield)* $2.523 million $2.608 million

Net capital cost† $7.477 million $9.392 million

EAC of net capital cost* $2.074 million $1.891 million

*Annuity discounted at 12%; number of years = project life. †Investment – PV(depreciation tax shield).

Project Evaluation


Problem 9.24 5

The present value of the depreciation tax shield for each alternative is computed as follows:

𝑃𝑉 = $0.700 million ×1

0.12‒

1

0.12 × 1+0.12 5= $2.523 𝑚𝑖𝑙𝑙𝑖𝑜𝑛

𝑃𝑉 = $0.525 million ×1

0.12‒

1

0.12 × 1+0.12 8= $2.608 𝑚𝑖𝑙𝑙𝑖𝑜𝑛

The equivalent annual cost (EAC) for each alternative is computed as follows:

𝑃𝑉 = C ×1

0.12‒

1

0.12 × 1+0.125 = $7.477 𝑚𝑖𝑙𝑙𝑖𝑜𝑛 => C = EAC = $2.074 million

𝑃𝑉 = C ×1

0.12‒

1

0.12 × 1+0.128 = $9.392 𝑚𝑖𝑙𝑙𝑖𝑜𝑛 => C = EAC = $1.891 million

Since the operating costs are the same, then Do-It-Right is preferred because it has the lower EAC.

Solution

Sensitivity Analysis


a. (Revenue – expenses) changes by $4 million – $2 million = $2 million.

After-tax profits increase by $2 million (1 – 0.35) = $1.3 million.

Because depreciation is unaffected, cash flow changes by the same amount.

b. Expenses increase from $7 million to $9 million.

After-tax income and cash flow decrease by:

$2 million (1 – 0.35) = $1.3 million

A project currently generates sales of $10 million, variable costs equal to 50% of sales, and fixed costs of $2

million. The firm's tax rate is 35%. What are the effects of the following changes on after-tax profits and cash

flow? (a) Sales increase from $10 to $14 million (b) Variable costs increase to 70% of sales.

Chapter 10 6

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