Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate)
Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate)
9th Edition
ISBN: 9781259277214
Author: Stephen A. Ross Franco Modigliani Professor of Financial Economics Professor, Randolph W Westerfield Robert R. Dockson Deans Chair in Bus. Admin., Bradford D Jordan Professor
Publisher: McGraw-Hill Education
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Chapter 9, Problem 23QP

Project Analysis. You are considering a new product launch. The project will cost $780,000, have a four-year life, and have no salvage value; depreciation is straight-line to zero. Sales are projected at 180 units per year; price per unit will be $16,300, variable cost per unit will be $11,100, and fixed costs will be $535,000 per year. The required return on the project is 11 percent, and the relevant tax rate is 35 percent.

a. Based on your experience, you think the unit sales, variable cost, and fixed cost projections given here are probably accurate to within ±10 percent. What are the best and worst cases for these projections? What is the base-case NPV? What are the best-case and worst-case scenarios?

b. Evaluate the sensitivity of your base-case NPV to changes in fixed costs.

a)

Expert Solution
Check Mark
Summary Introduction

To calculate: The best and the worst case of the net present value.

Introduction:

The process of analyzing the future proceedings compared to the figures of the net present value is scenario analysis. A project often experiences the best and the worst case of scenarios.

Answer to Problem 23QP

The best case of the net present value is $980,214.89 and the worst case of the net present value is -$418,874.44.

Explanation of Solution

Given information:

A project with 4-year life is being evaluated, the cost of the project is $780,000 and it has no salvage value. The depreciation is assumed to be a straight-line to zero over the project’s life. The projected sales is 180 units for one year.

The price for a unit is $16,300, the fixed cost for a year is $535,000, and the variable cost for a unit is $11,100. The rate of tax is 35% and the required return is 11%. The projections for the quantity, price, variable cost, and fixed costs are within 11%. The rate of tax is 35%.

Scenario Unit sales Variable cost Fixed costs
Base 180 $11,100 $535,000
Best 198 $9,990 $481,500
Worst 162 $12,120 $588,500

Formula to calculate the operating cash flow using the tax shield approach:

OCF = [PFC](1Tc)+Depreciation(Tc)

Here, Tc is the tax rate, P is the price per unit, v is the variable cost, Q refers to quantity, and FC is the fixed cost.

Computation of the base case of the operating cash flow:

OCFbase = [PFC](1Tc)+Depreciation(Tc)=[[[($16,300$11,100)(180)(535,000)](0.65)+$780,0004(0.35)]]=$328,900

Hence, the base case of the operating cash flow is $328,900.

Formula to calculate the net present value:

NPV=Present value of cash outflow+Present value of cash inflow

Note: As there are many years, PVIFA is used. PVIFA is the present value interest factor of annuity.

Computation of the base case of the net present value:

NPVbase=Present value of cash outflow+Present value of cash inflow=$780,000+$328,900(PVIFA11% 4years)=$780,000+$328,900(3.1024)=$240,379.36

Hence, the base case of the net present value is $240,379.36.

Computation of the worst case of the operating cash flow:

OCFworst = [PFC](1Tc)+Depreciation(Tc)=[[[($16,300$12,210)(162)(588,500)](0.65)+$780,0004(0.35)]]=$116,402

Hence, the worst case of the operating cash flow is $116,402.

Computation of the worst case of the net present value:

NPVworst=Present value of cash outflow+Present value of cash inflow=$780,000+$116,402(PVIFA11% 4years)=$780,000+$116,402(3.1024)=$418,874.44

Hence, the worst case of the net present value is -$418,874.44.

Formula to calculate the operating cash flow using the tax shield approach:

OCF = [PFC](1Tc)+Depreciation(Tc)

Here, Tc is the tax rate, P is the price per unit, Q refers to quantity, and FC is the fixed cost.

Computation of the best case of the operating cash flow:

OCFbest = [PFC](1Tc)+Depreciation(Tc)=[[[($16,300$9,990)(198)(481,500)](0.65)+$780,0004(0.35)]]=$567,372

Hence, the best case of the operating cash flow is $567,372.

Formula to calculate the net present value:

NPV=Present value of cash outflow+Present value of cash inflow

Computation of the best case of the net present value:

NPVbest=Present value of cash outflow+Present value of cash inflow=$780,000+$567,372(PVIFA11% 4years)=$780,000+$567,372(3.1024)=$980,214.89

Hence, the best case of the net present value is $980,214.89.

b)

Expert Solution
Check Mark
Summary Introduction

To evaluate: The sensitivity of the base-case net present value to the changes in fixed costs.

Introduction:

The process of analyzing the future proceedings compared to the figures of the net present value is scenario analysis. A project often experiences the best and the worst case of scenarios.

Answer to Problem 23QP

For each dollar, the fixed costs will increase and the NPV declines by $2.02.

Explanation of Solution

Given information:

A project with 4-year life is being evaluated, the cost of the project is $780,000 and it has no salvage value. The depreciation is assumed to be a straight-line to zero over the project’s life. The projected sales is 180 units for one year.

The price for a unit is $16,300, the fixed cost for a year is $535,000, and the variable cost for a unit is $11,100. The rate of tax is 35% and the required return is 11%. The projections for the quantity, price, variable cost, and fixed costs are within 11%. The rate of tax is 35%.

Note: To find the sensitivity of the net present value to the changes in fixed costs, other level of fixed costs is chosen. The chosen fixed cost is $545,000.

Formula to calculate the operating cash flow using the tax shield approach:

OCF = [PFC](1Tc)+Depreciation(Tc)

Here, Tc is the tax rate, P is the price per unit, Q refers to quantity, and FC is the fixed cost.

Computation of the operating cash flow:

OCF = [PFC](1Tc)+Depreciation(Tc)=[[[($16,300$11,100)(180)(545,000)](0.65)+$780,0004(0.35)]]=$322,400

Hence, the operating cash flow is $322,400.

Formula to calculate the net present value:

NPV=Present value of cash outflow+Present value of cash inflow

Computation the net present value:

NPV=Present value of cash outflow+Present value of cash inflow=$780,000+$322,400(PVIFA11% 4years)=$780,000+$322,400(3.1024)=$220,213.76

Hence, the net present value is $220,213.76.

Formula to compute the sensitivity of net present value to the changes in fixed costs:

ΔNPVΔFC=(NPVBaseNPV)(FCBaseFC)

Compute the sensitivity of net present value to the changes in fixed costs:

ΔNPVΔFC=(NPVBaseNPV)(FCBaseFC)=($240,379.36$220,213.76)($535,000$545,000)=$20,165.6$10,000=$2.02

Hence, the sensitivity of the NPV to the changes in fixed costs is -$2.02.

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Chapter 9 Solutions

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate)

Ch. 9.5 - Prob. 9.5ACQCh. 9.5 - What are some potential sources of value in a new...Ch. 9.6 - What are scenario and sensitivity analyses?Ch. 9.6 - Prob. 9.6BCQCh. 9.7 - Why do we say that our standard discounted cash...Ch. 9.7 - What are managerial options in capital budgeting?...Ch. 9.7 - Prob. 9.7CCQCh. 9 - Prob. 9.1CCh. 9 - Section 9.2What are sunk costs?Ch. 9 - Prob. 9.3CCh. 9 - Section 9.4If a firms current assets are 150,000,...Ch. 9 - A project has a positive NPV. What could drive...Ch. 9 - If a firms variable cost per unit estimate used in...Ch. 9 - Section 9.7Capital rationing exists when a company...Ch. 9 - Opportunity Cost. In the context of capital...Ch. 9 - Depreciation. Given the choice, would a firm...Ch. 9 - Prob. 3CTCRCh. 9 - Stand-Alone Principle. Suppose a financial manager...Ch. 9 - Prob. 5CTCRCh. 9 - Capital Budgeting Considerations. A major college...Ch. 9 - Prob. 7CTCRCh. 9 - Prob. 8CTCRCh. 9 - Prob. 9CTCRCh. 9 - Sensitivity Analysis and Scenario Analysis. What...Ch. 9 - LO19.11Marginal Cash Flows. A co-worker claims...Ch. 9 - Prob. 12CTCRCh. 9 - Forecasting Risk. What is forecasting risk? In...Ch. 9 - Options and NPV. What is the option to abandon?...Ch. 9 - Prob. 1QPCh. 9 - Relevant Cash Flows. Winnebagel Corp. currently...Ch. 9 - Prob. 3QPCh. 9 - Calculating OCF. Consider the following income...Ch. 9 - Calculating Depreciation. A piece of newly...Ch. 9 - Prob. 6QPCh. 9 - Prob. 7QPCh. 9 - Calculating Project OCF. Rolston Music Company is...Ch. 9 - Calculating Project OCF. H. Cochran, Inc., is...Ch. 9 - Calculating Project NPV. In the previous problem,...Ch. 9 - Calculating Project Cash Flow from Assets. In the...Ch. 9 - NPV and Modified ACRS. In the previous problem,...Ch. 9 - Project Evaluation. Kolbys Korndogs is looking at...Ch. 9 - Project Evaluation. Your firm is contemplating the...Ch. 9 - Project Evaluation. In the previous problem,...Ch. 9 - Prob. 16QPCh. 9 - Prob. 17QPCh. 9 - Sensitivity Analysis. We are evaluating a project...Ch. 9 - Prob. 19QPCh. 9 - Prob. 20QPCh. 9 - Cost-Cutting Proposals. CSM Machine Shop is...Ch. 9 - Sensitivity Analysis. Consider a three-year...Ch. 9 - Project Analysis. You are considering a new...Ch. 9 - Project Analysis. McGilla Golf has decided to sell...Ch. 9 - Project Evaluation. Aria Acoustics, Inc. (AAI),...Ch. 9 - Prob. 26QPCh. 9 - Conch Republic Electronics Conch Republic...Ch. 9 - Conch Republic Electronics Conch Republic...Ch. 9 - Conch Republic Electronics Conch Republic...Ch. 9 - Conch Republic Electronics Conch Republic...Ch. 9 - Conch Republic Electronics Conch Republic...Ch. 9 - Conch Republic Electronics Conch Republic...Ch. 9 - Conch Republic Electronics Conch Republic...Ch. 9 - Conch Republic Electronics Conch Republic...
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