Chapter 11, Problem 20QP

Project Analysis [LO1, 2] McGilla Golf has decided to sell a new line of golf clubs. The clubs will sell for $715 per set and have a variable cost of $385 per set. The company has spent $150,000 for a marketing study that determined the company will sell 75,000 sets per year for seven years. The marketing study also determined that the company will lose sales of 10,000 sets of its high-priced clubs. The high-priced clubs sell at $1,150 and have variable costs of $620. The company will also increase sales of its cheap clubs by 12,000 sets. The cheap clubs sell for $425 and have variable costs of $195 per set. The fixed costs each year will be $9,400,000. The company has also spent $1,000,000 on research and development for the new clubs. The plant and equipment required will cost $30,100,000 and will be depreciated on a straight-line basis. The new clubs will also require an increase in net working capital of $1,400,000 that will be returned at the end of the project. The tax rate is 40 percent, and the cost of capital is 10 percent. Calculate the payback period, the NPV, and the IRR.

Summary Introduction

To determine: The payback period

Introduction:

Payback period refers to the number of periods it will take to recover the initial investments.

Answer to Problem 20QP

The payback period is 3.35 times.

Explanation of Solution

Given information:

The new clubs sold $715 per set, and the number of sets sold is 75,000 set per year. The cheaper club was sold for $425 per set, and number of sets sold is 12,000 set per year. The expensive clubs was sold for $1,150 in which the company has lost sales of 10,000 sets.

The variable cost of the new club is $385 per set, variable cost of the expensive cub is $620, and the variable cost of the cheaper club is $195. The fixed costs each year is $9,400,000.

Steps to determine the payback period:

• Firstly, determine the total sales and total variable cost of each clubs separately. Then, sum up the total sales from the existing clubs and total variable costs from all the clubs.
• Secondly, prepare the pro forma income statement.
• Next, determine the operating cash flows (OFCs) by adding up the net income and depreciation.
• Finally, estimate the payback period using its formula.

Formulae:

The formula to calculate total sales:

$\text{Total sales}=\text{Sales per units}\times \text{Number of units sold}$

The formula to calculate total variable costs:

$\text{Total Variable costs}=\text{Variable costs per units}\times \text{Number of units of sold}$

The formula to calculate total sales of the entire clubs:

$\text{Total sales of all clubs}=\left(\begin{array}{l}\text{Total sales of new clubs}\\ \text{+ Total sales of expensive clubs}\\ +\text{Total sales of cheaper clubs}\end{array}\right)$

The formula to calculate total variable costs of the entire clubs:

$\text{Total variable costs of all clubs}=\left(\begin{array}{l}\text{Total variable costs of new clubs}\\ \text{+ Total variable costs of expensive clubs}\\ +\text{Total variable costs of cheaper clubs}\end{array}\right)$

Compute the total sales of new clubs:

$\begin{array}{c}\text{Total sales}=\text{Sales per units}\times \text{Number of units sold}\\ =\$715\times 75,000\\ =\$53,625,000\end{array}$

Hence, the total sales of the new clubs are $53,625,000.

Compute the total sales of expensive clubs:

$\begin{array}{c}\text{Total sales}=\text{Sales per units}\times \text{Number of units sold}\\ =\$1,150\times -10,000\\ =-\$11,500,000\end{array}$

Hence, the total sales of the expensive clubs are −$11,500,000.

Compute the total sales of cheaper clubs:

$\begin{array}{c}\text{Total sales}=\text{Sales per units}\times \text{Number of units sold}\\ =\$425\times 12,000\\ =\$5,100,000\end{array}$

Hence, the total sales of the cheaper clubs are $5,100,000.

Compute the total sales of the entire clubs:

$\begin{array}{c}\text{Total sales of all clubs}=\left(\begin{array}{l}\text{Total sales of new clubs}\\ \text{+ Total sales of expensive clubs}\\ +\text{Total sales of cheaper clubs}\end{array}\right)\\ =\$53,625,000+\left(-\$11,500,000\right)+\$5,100,000\\ =\$53,625,000-\$11,500,000+\$5,100,000\\ =\$47,225,000\end{array}$

Hence, the total sales of the entire clubs are $47,225,000.

Table that indicating the entire sales for clubs:

Particulars	Variable cost per sets (in $) (A)	Number of sets Sold (in units) (B)	Total sales (in $) (C)=(A)×(B)
New clubs	715	75,000	53,625,000
Expensive clubs	1,150	(10,000)	(11,500,000)
Cheaper clubs	425	12,000	5,100,000
Total sales			47,225,000

Hence, the total sales for the entire clubs are $47,225,000.

Compute total variable costs of new clubs:

$\begin{array}{c}\text{Total variable costs}=\text{Variable costs per units}\times \text{Number of units of sold}\\ =-\$385\times 75,000\\ =-\$28,875,000\end{array}$

Hence, the total variable costs of the new clubs are −$28,875,000.

Compute total variable costs of expensive clubs:

$\begin{array}{c}\text{Total Variable costs}=\text{Variable costs per units}\times \text{Number of units of sold}\\ =\left(-\$620\right)\times \left(-10,000\right)\\ =\$6,200,000\end{array}$

Hence, the total variable costs of the expensive clubs are $6,200,000.

Compute total variable costs of cheaper clubs:

$\begin{array}{c}\text{Total variable costs}=\text{Variable costs per units}\times \text{Number of units of sold}\\ =\left(-\$195\right)\times 12,000\\ =-\$2,340,000\end{array}$

Hence, the total variable costs of the cheaper clubs are -$2,340,000.

Compute the total variable costs of the entire clubs:

$\begin{array}{c}\text{Total variable costs of all clubs}=\left(\begin{array}{l}\text{Total variable costs of new clubs}\\ \text{+ Total variable costs of expensive clubs}\\ +\text{Total variable costs of cheaper clubs}\end{array}\right)\\ =\left(-\$28,875,000\right)+\$6,200,000+\left(-\$2,340,000\right)\\ =\left(-\$22,675,000\right)-\$2,340,000\\ =-\$25,015,000\end{array}$

Hence, the total variable costs of the entire clubs are -$25,015,000.

Table indicating the variable costs:

Particulars	Variable cost per set (in $) (A)	Number of sets Sold (in units) (B)	Total variable costs (in $) (C)=(A)×(B)
New clubs	($385)	75,000	($28,875,000)
Expensive clubs	($620)	(10,000)	$6,200,000
Cheaper clubs	($195)	12,000	($2,340,000)
Total variable costs			($25,015,000)

Hence, the variable costs for the clubs are −$25,015,000.

Note: In order to prepare the pro forma income statement, depreciation of plant and equipment, earnings before interest and taxes (EBIT), and tax have to be computed to ascertain the net income from this statement.

The formula to calculate depreciation of plant and equipment:

$\text{Depreciation expense}=\frac{\text{Cost of the assets}}{\text{Useful life}}$

The formula to calculate EBIT:

$\text{EBIT}=\text{Sales}-\left(\text{Variable costs}+\text{Fixed costs}+\text{Depreciation}\right)$

The formula to calculate tax when tax rate is given:

$\text{Tax}=\text{EBIT}\times \text{Tax rate}$

The formula to calculate the net income:

$\text{Net income}=\text{EBIT}-\text{Tax}$

Compute depreciation expense of plant and equipment:

$\begin{array}{c}\text{Depreciation expense}=\frac{\text{Cost of the assets}}{\text{Useful life}}\\ =\frac{\$30,100,000}{7}\\ =\$4,300,000\end{array}$

Hence, the depreciation expense is $4,300,000.

Compute the EBIT:

$\begin{array}{c}\text{EBIT}=\text{Sales}-\left(\text{Variable costs}+\text{Fixed costs}+\text{Depreciation}\right)\\ =\$47,225,000-\left(25,015,000+ 9,400,000+4,300,000\right)\\ =\$47,225,000-\$38,715,000\\ =\$8,510,000\end{array}$

Hence, the EBIT is $8,510,000.

Compute tax when tax rate is given:

$\begin{array}{c}\text{Tax}=\text{EBIT}\times \text{Tax rate}\\ =\$8,510,000\times \left(\frac{40}{100}\right)\\ =\$8,510,000\times 0.40\\ =\$\text{3,404,000}\end{array}$

Hence, the tax is $3,404,000.

Compute the net income:

$\begin{array}{c}\text{Net income}=\text{EBIT}-\text{Tax}\\ =\$8,510,000-\$3,404,000\\ =\$5,106,000\end{array}$

Hence, the net income is $5,106,000.

Table indicating the pro forma income statement:

Pro forma income statement
Particulars	Amounts (in $)
Sales	47,225,000
Variable costs	25,015,000
Fixed costs	9,400,000
Depreciation	4,300,000
Earnings before interest and taxes	8,510,000
Taxes	3,404,000
Net income	5,106,000

Hence, the net income as per the pro forma income statement is $5,106,000.

Note: After preparing the pro forma income statement, determine the operating cash flow (OCF) and NPV to find out the sensitivity of the NPV to changes in the price of the new club.

The formula to calculate OCF:

$\text{OCF}=\text{Net income}+\text{Depreciation}$

Compute the operating cash flow (OCF):

$\begin{array}{c}\text{OCF}=\text{Net income + Depreciation}\\ =\$5,106,000+\$4,300,000\\ =\$9,406,000\end{array}$

Hence, the OCF is $9,406,000.

Now, determine the total investment

The formula to calculate the total investment:

$\text{Total investment}=\text{Total cost of assets}+\text{Net working capital}$

Compute the total investment:

$\begin{array}{c}\text{Total investment}=\text{Total cost of assets}+\text{Net working capital}\\ =\$30,100,000+\$1,400,000\\ =\$31,500,000\end{array}$

Hence, the total investment is $31,500,000.

Now, determine the accumulated net cash inflows for 7 years.

Years	Net Cash Outflows	Net Cash Inflows
	Amount invested	Annual	Accumulated
0	$31,500,000
1		$9,406,000	$9,406,000
2		$9,406,000	$18,812,000
3		$9,406,000	$28,218,000
4		$9,406,000	$37,624,000
5		$9,406,000	$47,030,000
6		$9,406,000	$56,436,000
7		$9,406,000	$65,842,000

Note: By the end of the year 3, the recovery amount is shorter than the total initial investment. In the year 4, the recovery amount is higher than total initial investment. It means that the payback period will be in between the years 3 and 4. As a result, estimate the amount needed to complete recovery in Year 4 by deducting accumulated net cash inflows at the end of Year 3 from the total investment amount.

The formula to calculate the amount needed to complete recovery in Year 4:

$\begin{array}{l}\text{Amount needed to complete}\\ \text{ recovery in Year 4}\end{array}\}=\left(\begin{array}{l}\text{Total invested amount}-\\ \text{Accumulated net cash}\text{inflows at the end of Year 3}\end{array}\right)$

The formula to calculate the payback period:

$\text{Pay back period}=\text{Number of project line}+\left(\frac{\text{Total investment}}{\text{Operating cash flows}}\right)$

Compute the amount needed to complete recovery in Year 4:

$\begin{array}{c}\begin{array}{l}\text{Amount needed to complete}\\ \text{ recovery in Year 4}\end{array}\}=\left(\begin{array}{l}\text{Total invested amount}-\\ \text{Accumulated net cash}\text{inflows at the end of Year 3}\end{array}\right)\\ =\$31,500,000-\$28,218,000\\ =\$3,282,000\end{array}$

Hence, the amount needed to complete recovery in Year 4 is $3,282,000.

Compute the payback period:

$\begin{array}{c}\text{Pay back period}=\text{Number of project line}+\left(\frac{\text{Total investment}}{\text{Operating cash flows}}\right)\\ =3+\left(\frac{\$3,282,000}{\$9,406,000}\right)\\ =3+0.35\\ =3.35\text{ years}\end{array}$

Hence, the payback period is 3.35 years.

Summary Introduction

To determine: The net present value (NPV)

Introduction:

Net present value (NPV) refers to the current discounted value of the future cash flows. The company should accept the project, if the net present value is positive or greater than zero and vice-versa. If there are two mutually exclusive projects, then the company has to select the project that has higher net present value.

Answer to Problem 20QP

The net present value (NPV) is $15,010,782.5.

Explanation of Solution

Given information:

The cost of capital is 10% and the project lifetime is 7 years.

The formula to calculate the present value of OCF:

$\text{Present value of OCF}=\text{OCF}\times \left(\begin{array}{l}\text{Present value of an annuity}\\ \text{ of \$1 period for R\% of N period}\end{array}\right)$

The formula to calculate the present value of the net working capital:

$\text{Present value of net working capital}=\frac{\text{Net working capital }}{{\left(\text{1}+\text{Cost of capital}\right)}^{\text{t}}}$

Where,

t refers to the project lifetime

The formula to calculate the NPV:

$\text{NPV}=\left[\begin{array}{c}\left(\text{Present value of OCF}+\text{Present value of net working capital}\right)\\ -\left(\text{Initial cost of project +Working capital investment}\right)\end{array}\right]$

Compute the present value of OCF:

Note: To determine the present value of annuity of $1 period for 7 period at a discount rate of 10%, refer the PV of an annuity of $1 table. Then find out 10% discount rate and period of 7 years value from the table. Here, the value for the rate 10% and 7 years period the value is 4.86842.

$\begin{array}{c}\text{Present value of OCF}=\text{OCF}\times \left(\begin{array}{l}\text{Present value of an annuity}\\ \text{ of \$1 period for R\% of N period}\end{array}\right)\\ =\$9,406,000\times \left(\begin{array}{l}\text{Present value of an annuity }\\ \text{of }\$1\text{ period for }10\%\text{ of }7\text{ period}\end{array}\right)\\ =\$9,406,000\times 4.86842\\ =\$45,792,358.52\end{array}$

Hence, the present value of OCF is $45,792,358.52.

Compute the present value of the net working capital:

$\begin{array}{c}\text{Present value of net working capital}=\frac{\text{Net working capital }}{{\left(\text{1}+\text{Cost of capital}\right)}^{\text{t}}}\\ =\frac{\$1,400,000}{{\left(1+0.10\right)}^7}\\ =\frac{\$1,400,000}{{\left(1.10\right)}^7}\end{array}$

$\begin{array}{c}=\frac{\$1,400,000}{1.94871}\\ =\$718,423.98\end{array}$

Hence, the present value of net working capital is $718,423.98.

Compute the net present value:

$\begin{array}{c}\text{NPV}=\left[\begin{array}{c}\left(\text{Present value of OCF}+\text{Present value of net working capital}\right)\\ -\left(\text{Initial cost of project +Working capital investment}\right)\end{array}\right]\\ =\left[\left(\$45,792,358.52+\$718,423.98\right)-\left(\$30,100,000+\$1,400,000\right)\right]\\ =\$46,510,782.5-\$31,500,000\\ =\$15,010,782.5\end{array}$

Hence, the NPV is $15,010,782.5.

Summary Introduction

To determine: The Internal rate of return (IRR)

Introduction:

Internal rate of return (IRR) is a projected rate of return for a particular project based on the given incremental cash flows of the project. This method considers all the cash flows of the particular project and adjusts for time value of money like net present value.

Answer to Problem 20QP

The IRR is 23.15%.

Explanation of Solution

Given information:

The net working capital is $1,400,000, and fixed costs each year is $9,400,000.  The cost of capital is 10% and the number of years is 7 years.

The steps to calculate the IRR using the Excel sheet:

• Firstly, specify the total investment made of the year and show the net annual cash inflows for seven years in a tabular format as given below.
• Then, add net working capital with the initial cash flow in the seventh year.
• Finally, use Excel function “IRR (values, [guess])” to determine the internal rate of return. The values indicate the entire cash flows, and guess indicates the percentage of cost of capital.

Compute the IRR:

Particulars	Amount
Total investment	($31,500,000)
First year cash flow	$9,406,000
Second year cash flow	$9,406,000
Third year cash flow	$9,406,000
Forth year cash flow	$9,406,000
Fifth year cash flow	$9,406,000
Sixth year cash flow	$9,406,000
Seventh year cash flow	10,806,000.00
Internal rate of return (IRR)	23.15%

Hence, the IRR is 23.15%.