Question

The Tuff Wheels was getting ready to start its development project for a new product to be added to their small motorized vehicle line for children. The new product is called the Kiddy Dozer. It will look like a miniature bulldozer, complete with caterpillar tracks and a blade. Tuff Wheels has forecasted the demand and the cost to develop and produce the new Kiddy Dozer. The table below contains the relevant information for this project.

Development cost	$	1,250,000
Estimated development time		9	months
Pilot testing	$	200,000
Ramp-up cost	$	400,000
Marketing and support cost	$	150,000	per year
Sales and production volume		60,000	per year
Unit production cost	$	100
Unit price	$	205
Interest rate		8	%

Tuff Wheels also has provided the project plan shown below. As can be seen in the project plan, the company thinks that the product life will be three years until a new product must be created.

Assume all cash flows occur at the end of each period.

a. What is the net present value (discounted at 8%) of this project? Consider all costs and expected revenues. (Enter your answer in thousands of dollars. Perform all calculations using Excel. Do not round any intermediate calculations. Round your answer to the nearest thousand.)

b. What is the impact on NPV for the Kiddy Dozer if the actual sales are 50,000 per year? 70,000 per year? (Enter your answer in thousands of dollars. Perform all calculations using Excel. Do not round any intermediate calculations. Round your answer to the nearest thousand.)

c. Based on the original sales level of 60,000, what is the effect on NPV caused by changing the discount rate to 9%, 10%, or 11%? (Enter your answer in thousands of dollars. Perform all calculations using Excel. Do not round any intermediate calculations. Round your answer to the nearest thousand.)

Answer 1

The yearly cash flows can be calculated based on the project plan provided in the question.

Cash outflow as per project plan :

Development costs - First three-quarters of year 1

Pilot testing - Q4 of year 1 and Q1 of year 2

Ramp up cost- Q4 of year 1 and Q1 of year 2

For Financial analysis and discounting we presume as below:

Development cost - fully incurred at the end of year 1

Pilot testing cost - fully incurred at the end of year 1

Ramp up cost - fully incurred at the end of year 1

Project inflows, however, start from Q2 of year 2

Hence production and Sales for Year 2 taken for only 3 quarters = 60000 units * 3/4 = 45000 units

Sales in Dollars for the year 2 would be = 45000 * 170= $7,650,000

Production cost for year 2 = 45000 * 100 = $4,500,000

Units for year 3 and 4 would be 60,000 units each

Sales in Dollars would be = 60,000 * 170 = $10,200,000 for each year

Production cost would be = 60,000 * 100 =$6,000,000 for each year

Now the yearly cash flow chart will be as follows:

Description	Year 1	Year 2	Year 3	Year 4	Net present value
Sales in $ (A)	0	89,25,000	1,19,00,000	1,19,00,000
Development cost($) (B)	10,00,000
Pilot testing($) (C)	2,00,000
Ramp-up cost($)(D)	4,00,000
Production cost($)(E)	0	52,50,000	70,00,000	70,00,000
Marketing cost($) (F)	0	1,50,000	1,50,000	1,50,000
Cash flows($){A- (B+C+D+E+F)}	(-)1,600,000	35,25,000	47,50,000	47,50,000
Present value Discounting factor @8%	0.926	0.857	0.794	0.735
Present value($)	(-)1,481,600	30,20,925	37,71,500	34,91,250	$8,802,075

Generally, it is provided that the initial expenses(development cost etc) are incurred at the outset and the revenues and related costs are incurred at the end of the year. But in the given problem based on the project plan, it is assumed that the expenses are incurred at the end of year 1 and then the revenue and production and related costs are incurred from year 2. Hence discounting is done for both the initial expenses as well as the subsequent yearly cash flows to ascertain Net present value as of the beginning of year1.

For 50,000 units the necessary calculation are as follows:

As production starts in Q2 of year 2 production volume for year 2 = 50000 * 3/4 = 37500 units;

Sales value in $ for year 2 = 37,500 * 170 = $6,375,000;

Production cost in $ for year 2= 37,500 * 100 =$ 3,750,000;

For year 3 and year 4 the sales value and production cost for 50,000 units would be:

Sales in $ = 50,000 * 170 = $8,500,000

Production cost in $ = 50,000 * 100= $5,000,000

Calculation of NPV for 50,000 units :

Description	Year 1	Year 2	Year 3	Year 4	Net present value
Sales in $ (A)	0	63,75,000	85,00,000	85,00,000
Development cost($) (B)	10,00,000
Pilot testing($) (C)	2,00,000
Ramp-up cost($)(D)	4,00,000
Production cost($)(E)	0	37,50,000	50,00,000	50,00,000
Marketing cost($) (F)	0	1,50,000	1,50,000	1,50,000
Cash flows($){A- (B+C+D+E+F)}	(-)1,600,000	24,75,000	33,50,000	33,50,000
Present value Discounting factor @8%	0.926	0.857	0.794	0.735
Present value($)	(-)1,481,600	21,21,075	26,59,900	24,62,250	$5,761,625

For production volume = 70,000units,

As production starts in Q2 of year 2 production volume for year 2 = 70,000 * 3/4 = 52,500 units

Sales value in $ for year 2 = 52,500 * 170= $8,925,000

Production cost in $ for year 2= 52,500 * 100 = $5,250,000

For year 3 and year 4 the sales value and production cost for 70,000 units would be:

Sales in $ = 70,000 * 170 = $11,900,000

Production cost in $ = 70,000 * 100 =$7,000,000

Calculation of NPV for 70,000 units :

Description	Year 1	Year 2	Year 3	Year 4	Net present value
Sales in $ (A)	0	89,25,000	1,19,00,000	1,19,00,000
Development cost($) (B)	10,00,000
Pilot testing($) (C)	2,00,000
Ramp-up cost($)(D)	4,00,000
Production cost($)(E)	0	52,50,000	70,00,000	70,00,000
Marketing cost($) (F)	0	1,50,000	1,50,000	1,50,000
Cash flows($){A- (B+C+D+E+F)}	(-)1,600,000	35,25,000	47,50,000	47,50,000
Present value Discounting factor @8%	0.926	0.857	0.794	0.735
Present value($)	(-)1,481,600	30,20,925	37,71,500	34,91,250	$8,802,075

So the impact on NPV due to change in volume would be as follows:

Description	50000 units	70,000units
NPV at 60,000 units	$7,281,850	$7,281,850
NPV	$5,761,625	$8,802,075
Difference	$1,520,225(decrease)	$1,520,225(increase)

From the above, it can be seen that NPV at 50,000 units reduces by $1,520,225 while for 70,000units it increases by $1,520,225

For 9% interest rate the calculation is as follows :

Description	Year 1	Year 2	Year 3	Year 4	Net present value
Sales in $ (A)	0	76,50,000	1,02,00,000	1,02,00,000
Development cost($) (B)	10,00,000
Pilot testing($) (C)	2,00,000
Ramp-up cost($)(D)	4,00,000
Production cost($)(E)	0	45,00,000	60,00,000	60,00,000
Marketing cost($) (F)	0	1,50,000	1,50,000	1,50,000
Cash flows($){A- (B+C+D+E+F)}	16,00,000	30,00,000	40,50,000	40,50,000
Present value Discounting factor @9%	0.917	0.842	0.772	0.708
Present value($)	(-)1,467,889	25,25,040	31,27,343	28,69,122	$7,053,616

For 10% interest rate the calculation is as follows :

Description	Year 1	Year 2	Year 3	Year 4	Net present value
Sales in $ (A)	0	76,50,000	1,02,00,000	1,02,00,000
Development cost($) (B)	10,00,000
Pilot testing($) (C)	2,00,000
Ramp-up cost($)(D)	4,00,000
Production cost($)(E)	0	45,00,000	60,00,000	60,00,000
Marketing cost($) (F)	0	1,50,000	1,50,000	1,50,000
Cash flows($){A- (B+C+D+E+F)}	16,00,000	30,00,000	40,50,000	40,50,000
Present value Discounting factor @10%	0.909	0.826	0.751	0.683
Present value($)	(-)1,454,545	24,79,339	30,42,825	27,66,204	$6,833,823

For 11% interest rate the calculation is as follows :

Description	Year 1	Year 2	Year 3	Year 4	Net present value
Sales in $ (A)	0	76,50,000	1,02,00,000	1,02,00,000
Development cost($) (B)	10,00,000
Pilot testing($) (C)	2,00,000
Ramp-up cost($)(D)	4,00,000
Production cost($)(E)	0	45,00,000	60,00,000	60,00,000
Marketing cost($) (F)	0	1,50,000	1,50,000	1,50,000
Cash flows($){A- (B+C+D+E+F)}	16,00,000	30,00,000	40,50,000	40,50,000
Present value Discounting factor @11%	0.901	0.812	0.731	0.659
Present value($)	(-)1,441,441	24,34,867	29,61,325	26,67,860	$6,622,611