Question

​(Net present value​ calculation) Big​ Steve's, makers of swizzle​ sticks, is considering the purchase of a new plastic stamping machine. This investment requires an initial outlay of

​$110,000 and will generate net cash inflows of ​$17,000 per year for 8 years.

a. What is the​ project's NPV using a discount rate of 8 percent​? Should the project be​ accepted? Why or why​ not?

b. What is the​ project's NPV using a discount rate of 17 ​percent? Should the project be​ accepted? Why or why​ not?

c. What is this​ project's internal rate of​ return? Should the project be​ accepted? Why or why​ not?

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a. If the discount rate is 8 ​percent, then the​ project's NPV is ​$(?). ​(Round to the nearest​ dollar.)

The project ▼ (should not be, should be) accepted because the NPV is ▼ (negative, positive) and therefore (does not add, adds)  value to the firm. 

b. If the discount rate is 17 ​percent, then the​ project's NPV is ​$(?). (Round to the nearest​ dollar.)

The project (should be, should not be) accepted because the NPV is (positive, negative) and therefore (does not add, adds) value to the firm. 

c. This​ project's internal rate of return is (?)​%​. (Round to two decimal​ places.)

If the​ project's required discount rate is 8​%, then the project (should be, should not be) ​accepted, because the IRR is (lower than, higher than) the required discount rate.  

If the​ project's required discount rate is 17​%, then the project (should not be, should be) ​accepted, because the IRR is (lower than, higher than) the required discount rate.  

Answer 1

NPV

NPV = Initial cash outlay + PV of all the cash inflows

PV of cash flow at time n = Cash flow at time n/ ((1+r)^n)

IRR

IRR is the interest rate at which NPV = 0

0 = -CF0 + (CF1/((1+IRR)^1)) + (CF2/((1+IRR)^2)) + (CF3/((1+IRR)^3)) + (CF4/((1+IRR)^4)) +...... + (CF8/((1+IRR)^8))

Initial cash flow = -​$110,000

Cash flow from year 1 to year 8 = $17,000

a) Discount rate = 8%

Years	Cash Flows	PV
0	(110,000)	(110,000.0)
1	17,000	15,740.7
2	17,000	14,574.8
3	17,000	13,495.1
4	17,000	12,495.5
5	17,000	11,569.9
6	17,000	10,712.9
7	17,000	9,919.3
8	17,000	9,184.6
Discount rate	8.00%
NPV	(12,307.14)

Project should not be accepted as the project's NPV is less than 0

b) Discount rate = 17%

Years	Cash Flows	PV
0	(110,000)	(110,000.0)
1	17,000	14,529.9
2	17,000	12,418.7
3	17,000	10,614.3
4	17,000	9,072.1
5	17,000	7,753.9
6	17,000	6,627.3
7	17,000	5,664.3
8	17,000	4,841.3
Discount rate	17.00%
NPV	(38,478.24)

Project should not be accepted as the project's NPV is less than 0

c) 0 = -110,000+ (17,000/((1+IRR)^1)) + (17,000/((1+IRR)^2)) + (17,000/((1+IRR)^3)) + (17,000/((1+IRR)^4)) +...... + (17,000/((1+IRR)^8))

Solving for IRR = 4.97%

Project should not be accepted as the project's IRR is less than 8% and 17%

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a. If the discount rate is 8 ​percent, then the​ project's NPV is ​$(12,307.14). ​(Round to the nearest​ dollar.)

The project should not be accepted because the NPV is negative and therefore does not add value to the firm. 

b. If the discount rate is 17 ​percent, then the​ project's NPV is ​$(38,478.24). (Round to the nearest​ dollar.)

The project should not be accepted because the NPV is negative and therefore does not add value to the firm.

c. This​ project's internal rate of return is 4.97​%​. (Round to two decimal​ places.)

If the​ project's required discount rate is 8​%, then the project should not be ​accepted, because the IRR is lower than the required discount rate.  

If the​ project's required discount rate is 17​%, then the project should not be ​accepted, because the IRR is lower than the required discount rate.