Question

Perform a sensitivity analysis for the effects of key variables (e.g., sales growth rate, cost of capital, unit costs, sales price) on the estimated NPV or IRR in order to demonstrate the sensitivity of the model. The Scenario analysis of several variables simultaneously is encouraged (but not required).

Answer 1

Several steps are involved in sensitivity analysis of a project.

1. Determine input and output variables.

2. Calculate the baseline value of the output variable using the baseline input variables value.

3. Change the value of one of the input variables while others remain constant, and calculate the new value of the output variable.

4. Calculate the percentage change of both output and input variable compared to baseline values.

5. Calculate the sensitivity of the output variable to the change in the input variable using the formula below.

Formula

Sensitivity =	% change in output
% change in input

Steps three through five should be repeated for the other input variables.

Sensitivity analysis allows identification of input variables that represent the greatest vulnerability for the project.

Example

A company is considering a project with initial costs of $500,000 involving purchase of new machinery with a useful life of 5 years. The after-tax cost of capital is 16%, and the marginal tax rate is 30%. The other key parameters of a project are presented in the table below.

The depreciation expense of $40,000 per annum is included in fixed costs.

The management of a company will conduct sensitivity analysis of a project.

Solution

Step 1

Management designates the net present value (NPV) and the internal rate of return (IRR) as outputs. The inputs are:

· Fixed costs

· Sales in units

· Sales price per unit

· Variable costs per unit

Step 2

Let’s find the baseline NPV and IRR. The calculation of discounted cash flows is shown in the table below.

The calculation of discounted net cash flow for designated Year 1 is shown below.

S = 20,000 × $35 = $700,000

TVC = 20,000 × $22 = $440,000

EBT = $700,000 - $440,000 - $100,000 = $160,000

T = $160,000 × 30% = $48,000

NI = $160,000 - $48,000 = $112,000

NCF = $112,000 + $40,000 = $152,000

DNCF =	$152,000	= $131,034
(1+0.16)1

The discounted net cash flows in other designated years are calculated in the same manner.

The baseline net present value of a project is as follows:

Baseline NPV = -$500,000 + $131,034 + $136,891 + $160,164 + $137,686 + $111,030 = $176,805

The baseline IRR is 29.03%.

Step 3

Let’s assume that fixed costs will be 5% higher than baseline values. Provided other inputs remain constant, the discounted net cash flows will be as follows:

NPV = -$500,000 + $128,017 + $134,238 + $157,810 + $135,579 + $109,113 = $164,757

% change in NPV =	$164,757 - $176,805	= -6.81%
$176,805

Sensitivity of NPV =	-6,81%	= -1.362
5%

This means that with an increase in fixed costs of 1%, the NPV of a project will decrease by 1.362%, and vice versa, if fixed costs are reduced by 1%, the NPV will increase by 1.362%.

The new value of IRR is 28.17%

% change in IRR =	28.17%-29.03%	= -2.96%
29.03%

Sensitivity of IRR =	-2.96%	= -0.592
5%

Step 4

Let’s assume that sales in units will be 5% higher than baseline values. Provided other inputs remain constant, the discounted net cash flows will be as follows:

Please note that the change in the number of units sold affects both sales and total variable costs figures!

NPV = -$500,000 + $138,879 + $144,902 + $169,246 + $145,573 + $117,545 = $216,145

% change in NPV =	$216,145 - $176,805	= 22.25%
$176,805

Sensitivity of NPV =	22.25%	= 4.450
5%

Thus, an increase in sales by 1% will cause an increase in NPV by 4.450% and vice versa.

The new value of IRR is 31.73%

% change in IRR =	31.73%-29.03%	= 9.30%
29.03%

Sensitivity of IRR =	9.30%	= 1.860
5%

Step 5

Let’s assume that the sales price of a unit will be 5% higher than baseline values. Provided other inputs remain constant, the discounted net cash flows will be as follows:

Please note that the change in sales price affects sales figures only!

NPV = -$500,000 + $152,155 + $157,491 + $183,170 + $157,896 + $128,277 = $278,989

% change in NPV =	$278,989-$176,805	= 57.79%
$176,805

Sensitivity of NPV =	57.79%	= 11.558
5%

An increase in the sales price by 1% will result in an increase in the NPV by 11.558%, and if the sales price drops by 1%, the NPV of a project will decrease by 11.558%.

The new value of IRR is 35.95%

% change in IRR =	35.95%-29.03%	= 23.84%
29.03%

Sensitivity of IRR =	9.30%	= 4.768
5%

Step 6

Let’s assume that variable costs per unit will be 5% higher than baseline values. Provided other inputs remain constant, the discounted net cash flows will be as follows:

NPV = -$500,000 + $117,759 + $124,301 + $146,240 + $125,363 + $100,298 = $113,961

% change in NPV =	$113,961 - $176,805	= -35.54%
$176,805

Sensitivity of NPV =	-35,54%	= -7.109
5%

An increase in the variable costs per unit by 1% will result in an decrease in the NPV by 7.109% and vice versa.

The new value of IRR is 24.57%

% change in IRR =	24.57% - 29.03%	= -15.36%
29.03%

Sensitivity of IRR =	-15.36%	= -3.072
5%

Results of sensitivity analysis

Sensitivity analysis shows that the NPV and IRR of a project are most vulnerable to the change in the sales price and variable costs per unit and less vulnerable to the change in fixed costs and sales in units.