Question 2. When using the APV methodology, What is the NPV of the depreciation

Question

Question 2. When using the APV methodology, What is the NPV of the depreciation tax shield?

a. $32,051.52

b. $25,777.35

c. $19,165.01

d. 97,152.98

e 5-year project requires equipment that costs $80,000. If undertaken, the shareholders will contribute $20,000 cash with an interest-only loan with a maturity of 5 years and annual interest payments. The equipment will be deprecated sraight-ine t nts Save Ar and boow 560 the 5-year life of the project. There will be a pre-tax salvage value of $3,200. There are no other stant-up costs at yearDuring yeans 1 through 5, the firm will sell 20,000 units of product at s5, variable costs are $2, there are no fived costs rade-8%, r,rsity = 20%, tax rate = 30% debt-to-equity ratio-3,r,-2% OCF-80,000 ocr_. = 20,000 r(5-2) x (1-30%) + 16,000 x 30 % 46,800 OCFS = 46,800 + 3,200 = 50,000 What is the NPV of the project using the WACC methodology? $58,028 68 $89,613.03 $97,108 16

Explanation / Answer

Question 1). Answer :- Option b). $ 89,613.03

Explanation :- Calculation of Net present value (NPV) of the project :-

WACC = Weight of equity * Cost of equity + Weight of debt * Cost of debt

= (20000 / 80000) * 20 % + (60000 / 80000) * 8 % * (1 - 0.30)

= 0.25 * 20 % + 0.75 * 5.60 %

= 5 % + 4.20 %

= 9.20 %

Calculation of the free cash flow of project :-

Sales revenue (20000 * 5)

(-) Variable costs (20000 * 2)

100000

40000

Contribution margin

(-) Fixed cost

  60000

0

Earnings before depreciation, interest and tax (EBDIAT)

(-) Depreciation expense (80000 / 5)

  60000

16000

Earnings before interest and tax (EBIT)

(-) Interest expense (60000 * 8 %)

  44000

4800

Earning before tax (EBT)

(-) Tax expense (30 % of 39200)

  39200

11760

Net income

(+) Depreciation

27440

16000

Present value of cash inflows = 43440 * [ 1 - (1 + 0.092)-5 ] / 0.092 + 3200 * (1 - 0.30) / (1 + 0.092)5

= 43440 * [ 1 - (1.092)-5 ] / 0.092 + 2240 / (1.092)5

= 43440 * [ 1 - 0.644 ] / 0.092 + 2240 / 1.5528

= 43440 * 0.356 / 0.092 + 1442.56

= 168093.91 + 1442.56

= $ 169536.47 (approx).

Present value of cash outflow = $ 80,000.

Net present value (NPV) of Project = 169536.47 - 80000 = $ 89536.47 (Most nearest to the $ 89,613.03 mentioned in option b to the given question).

Conclusion :- Net present value (NPV) of Project = $ 89,613.03 (Option b).

Question 2). Answer :- Option c). $ 19165.01

Explanation :- NPV of Depreciation Tax Shield = (80000 / 5) * 0.30 * [ 1 - (1 + 0.092)-5 ] / 0.092

= 16000 * 0.30 * [ 1 - (1.092)-5 ] / 0.092

= 4800 * (1 - 0.644) / 0.092

= 4800 * 0.356 / 0.092

= 4800 * 3.86957

= $ 18573.936 (Most nearest to the $ 19165.01 mentioned in option c to the given question).

Conclusion :- NPV of Depreciation Tax Shield = $ 19165.01 (Option c)

Particulars Amount ($)

Sales revenue (20000 * 5)

(-) Variable costs (20000 * 2)

100000

40000

Contribution margin

(-) Fixed cost

  60000

0

Earnings before depreciation, interest and tax (EBDIAT)

(-) Depreciation expense (80000 / 5)

  60000

16000

Earnings before interest and tax (EBIT)

(-) Interest expense (60000 * 8 %)

  44000

4800

Earning before tax (EBT)

(-) Tax expense (30 % of 39200)

  39200

11760

Net income

(+) Depreciation

27440

16000

Free cash flow 43440

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