Question

Bauer Industries is an automobile manufacturer. Management is currently evaluating a proposal to build a plant that will manufacture lightweight trucks. Bauer plans to use a cost of capital of 12.3 % to evaluate this project. Based on extensive​ research, it has prepared the following incremental free cash flow projections​ (in millions of​ dollars): a. For this​ base-case scenario, what is the NPV of the plant to manufacture lightweight​ trucks? b. Based on input from the marketing​ department, Bauer is uncertain about its revenue forecast. In​ particular, management would like to examine the sensitivity of the NPV to the revenue assumptions. What is the NPV of this project if revenues are 10 % higher than​ forecast? What is the NPV if revenues are 10 % lower than​ forecast? c. Rather than assuming that cash flows for this project are​ constant, management would like to explore the sensitivity of its analysis to possible growth in revenues and operating expenses.​ Specifically, management would like to assume that​ revenues, manufacturing​ expenses, and marketing expenses are as given in the table for year 1 and grow by 2 % per year every year starting in year 2. Management also plans to assume that the initial capital expenditures​ (and therefore​ depreciation), additions to working​ capital, and continuation value remain as initially specified in the table. What is the NPV of this project under these alternative​ assumptions? How does the NPV change if the revenues and operating expenses grow by 6 % per year rather than by 2 %​? d. To examine the sensitivity of this project to the discount​ rate, management would like to compute the NPV for different discount rates. Create a​ graph, with the discount rate on the x​-axis and the NPV on the y​-axis, for discount rates ranging from 5 % to 30 %. For what ranges of discount rates does the project have a positive​ NPV?

1.9 10 Year Revenues Manufacturing Expenses (other than depreciation) Marketing Expenses Depreciation EBIT Taxes at 34% Unlevered Net Income Depreciation Additions to Net Working Capital Capital Expenditures Continuation Value Free Cash Flow 105.0 34.1 105.0 34.1 - 15.2 46.3 - 15.742- 15.742 30.558 15.2 - 15.2 46.3 30.558 15.2 - 152.0 + 11.6 53.158 - 152.0 41.558

Answer 1

Since, there are multiple parts to the question and Part b and Part c have multiple subparts, I have answered the first three parts (a,b and c) completely..

______

Part a)

The NPV of the plant to manufacture lightweight​ trucks is calculated as below:

NPV = Capital Expenditures + Free Cash Flow Year 1/(1+Cost of Capital)^1 + Free Cash Flow Year 2/(1+Cost of Capital)^2 + Free Cash Flow Year 3/(1+Cost of Capital)^3 + Free Cash Flow Year 4/(1+Cost of Capital)^4 + Free Cash Flow Year 5/(1+Cost of Capital)^5 + Free Cash Flow Year 6/(1+Cost of Capital)^6 + Free Cash Flow Year 7/(1+Cost of Capital)^7 + Free Cash Flow Year 8/(1+Cost of Capital)^8 + Free Cash Flow Year 9/(1+Cost of Capital)^9 + Free Cash Flow Year 10/(1+Cost of Capital)^10

Using the values provided in the question in the above formula, we get,

NPV = -152 + 41.558/(1+12.3%)^1 + 41.558/(1+12.3%)^2 + 41.558/(1+12.3%)^3 + 41.558/(1+12.3%)^4 + 41.558/(1+12.3%)^5 + 41.558/(1+12.3%)^6 + 41.558/(1+12.3%)^7 + 41.558/(1+12.3%)^8 + 41.558/(1+12.3%)^9 + 53.158/(1+12.3%)^10 = $83.59 or $83.6 million

______

Part b)

When revenues are 10% higher than forecast

We will have to calculate revised free cash flow as below:

Year	0	1-9	10
Revenues (105 + 10%*105)		115.5	115.5
Manufacturing Expenses (Other than Depreciation)		-34.1	-34.1
Marketing Expenses		-9.4	-9.4
Depreciation		-15.2	-15.2
EBIT		56.8	56.8
Taxes at 34%		-19.312	-19.312
Unlevered Net Income		37.488	37.488
Depreciation		15.2	15.2
Additions to Net Working Capital		-4.2	-4.2
Capital Expenditures	-152
Continuation Value			11.6
Free Cash Flow	-152	48.488	60.088

Now, we can calculate NPV as below:

NPV = -152 + 48.488/(1+12.3%)^1 + 48.488/(1+12.3%)^2 + 48.488/(1+12.3%)^3 + 48.488/(1+12.3%)^4 + 48.488/(1+12.3%)^5 + 48.488/(1+12.3%)^6 + 48.488/(1+12.3%)^7 + 48.488/(1+12.3%)^8 + 48.488/(1+12.3%)^9 + 60.088/(1+12.3%)^10 = $122.27 or $122.3 million

______

When revenues are 10% lower than forecast

We will have to calculate revised free cash flow as below:

Year	0	1-9 Years	10
Revenues (105 - 10%*105)		94.5	94.5
Manufacturing Expenses (Other than Depreciation)		-34.1	-34.1
Marketing Expenses		-9.4	-9.4
Depreciation		-15.2	-15.2
EBIT		35.8	35.8
Taxes at 34%		-12.172	-12.172
Unlevered Net Income		23.628	23.628
Depreciation		15.2	15.2
Additions to Net Working Capital		-4.2	-4.2
Capital Expenditures	-152
Continuation Value			11.6
Free Cash Flow	-152	34.628	46.228

Now, we can calculate NPV as below:

NPV = -152 + 34.628/(1+12.3%)^1 + 34.628/(1+12.3%)^2 + 34.628/(1+12.3%)^3 + 34.628/(1+12.3%)^4 + 34.628/(1+12.3%)^5 + 34.628/(1+12.3%)^6 + 34.628/(1+12.3%)^7 + 34.628/(1+12.3%)^8 + 34.628/(1+12.3%)^9 + 46.228/(1+12.3%)^10 = $44.91 or $44.9 million

______

Part c)

When revenues and expenses grow by 2%

We will have to calculate revised free cash flow for each year as follows:

Year	0	1	2	3	4	5	6	7	8	9	10
Revenues		105.0	107.1	109.2	111.4	113.7	115.9	118.2	120.6	123.0	125.5
Manufacturing Expenses (Other than Depreciation)		-34.1	-34.8	-35.5	-36.2	-36.9	-37.6	-38.4	-39.2	-40.0	-40.8
Marketing Expenses		-9.4	-9.6	-9.8	-10.0	-10.2	-10.4	-10.6	-10.8	-11.0	-11.2
Depreciation		-15.2	-15.2	-15.2	-15.2	-15.2	-15.2	-15.2	-15.2	-15.2	-15.2
EBIT		46.3	47.5	48.8	50.1	51.4	52.7	54.1	55.4	56.9	58.3
Taxes at 34%		-15.742	-16.160	-16.587	-17.022	-17.466	-17.918	-18.380	-18.851	-19.331	-19.821
Unlevered Net Income		30.558	31.370	32.198	33.042	33.904	34.783	35.679	36.593	37.526	38.477
Depreciation		15.2	15.2	15.2	15.2	15.2	15.2	15.2	15.2	15.2	15.2
Additions to Net Working Capital		-4.2	-4.2	-4.2	-4.2	-4.2	-4.2	-4.2	-4.2	-4.2	-4.2
Capital Expenditures	-152
Continuation Value											11.6
Free Cash Flow	-152	41.558	42.370	43.198	44.042	44.904	45.783	46.679	47.593	48.526	61.077

Now, we can calculate NPV as below:

NPV = -152 + 41.558/(1+12.3%)^1 + 42.370/(1+12.3%)^2 + 43.198/(1+12.3%)^3 + 44.042/(1+12.3%)^4 + 44.904/(1+12.3%)^5 + 45.783/(1+12.3%)^6 + 46.679/(1+12.3%)^7 + 47.593/(1+12.3%)^8 + 48.526/(1+12.3%)^9 + 61.077/(1+12.3%)^10 = $100.53 or $100.5 million

______

When revenues and expenses grow by 5%

We will have to calculate revised free cash flow for each year as follows:

Year	0	1	2	3	4	5	6	7	8	9	10
Revenues		105.0	110.3	115.8	121.6	127.6	134.0	140.7	147.7	155.1	162.9
Manufacturing Expenses (Other than Depreciation)		-34.1	-35.8	-37.6	-39.5	-41.4	-43.5	-45.7	-48.0	-50.4	-52.9
Marketing Expenses		-9.4	-9.9	-10.4	-10.9	-11.4	-12.0	-12.6	-13.2	-13.9	-14.6
Depreciation		-15.2	-15.2	-15.2	-15.2	-15.2	-15.2	-15.2	-15.2	-15.2	-15.2
EBIT		46.3	49.4	52.6	56.0	59.6	63.3	67.2	71.3	75.7	80.2
Taxes at 34%		-15.742	-16.788	-17.885	-19.038	-20.248	-21.519	-22.853	-24.254	-25.726	-27.270
Unlevered Net Income		30.558	32.588	34.718	36.956	39.305	41.772	44.362	47.082	49.938	52.936
Depreciation		15.2	15.2	15.2	15.2	15.2	15.2	15.2	15.2	15.2	15.2
Additions to Net Working Capital		-4.2	-4.2	-4.2	-4.2	-4.2	-4.2	-4.2	-4.2	-4.2	-4.2
Capital Expenditures	-152
Continuation Value											11.6
Free Cash Flow	-152	41.558	43.588	45.718	47.956	50.305	52.772	55.362	58.082	60.938	75.536

Now, we can calculate NPV as below:

NPV = -152 + 41.558/(1+12.3%)^1 + 43.588/(1+12.3%)^2 + 45.718/(1+12.3%)^3 + 47.956/(1+12.3%)^4 + 50.305/(1+12.3%)^5 + 52.772/(1+12.3%)^6 + 55.362/(1+12.3%)^7 + 58.082/(1+12.3%)^8 + 60.938/(1+12.3%)^9 + 75.536/(1+12.3%)^10 = $129.15 or $129.1 million