RSM 333 Term Test Practice Problems and Solutions
Long and Short Answers
Question 1
A company is considering replacing some old equipment. The current market price of the old
equipment is $500,000 and the salvage value of the old equipment at the end of five years is
$150,000. The new equipment will cost $1,000,000 and could be sold at the end of five years
for $350,000. The new equipment requires an additional $40,000 of working capital which will
be released at the end of five years.
The new equipment is estimated to generate $500,000 in before-tax operating income in the
first year, compared with $300,000 for the old equipment. After the first year, these before tax
operating income amounts for both the old and new equipment would grow by 3% per annum.
Assume the tax rate is 40% and the discount rate is 10%. The old machine was purchased for
$1,000,000 five years ago.
Required:
a) (9 points)
Estimate the NPV of the replacement decision assuming that the asset class will remain
open and have a positive balance at the end of the five years.
a)
Δ Initial Cost = -1,000,000 – 40,000 + 500,000 = -540,000
Δ Pre-tax Operating Income = 500,000 – 300,000 = 200,000
Δ CCA per year = 130,000 – 85,000 = 45,000 [old machine depreciates by $850,000 over 10
years, the new machine by $650,000 over 5 years]
Δ Salvage Value at time 5 = 350,000 – 150,000 = 200,000
∆𝑃𝑉𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝐶𝑜𝑠𝑡 = −540,000
200,000(1 − 40%) 1 + 3% 5
∆𝑃𝑉𝑂𝑃𝐶𝐹 = [1 − ( ) ] = 480,312.01
10% − 3% 1 + 10%
45,000 ∗ 40% 1
∆𝑃𝑉𝑃𝑉 𝐶𝐶𝐴 𝑇𝑆 = [1 − ] = 68,234.16
10% (1 + 10%)5
200,000 + 40,000
∆𝑃𝑉𝐸𝐶𝐹 = = 149,021.12
(1 + 10%)5
∆𝑁𝑃𝑉𝑅𝑒𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 = −540,000 + 480,312.01 + 68,234.16 + 149,021.12 = 157,567.29
The NPV for replacement is positive, therefore the firm should replace the equipment.
1
, Question 2
The Chief Biomechanical Engineer (CBE) of a biotech startup company, Dr. Cecilia Disney, has
hired you as a consultant to evaluate a project. The engineering team and Dr. Disney are planning
to develop a new drug that may cure cancer. The company is expecting to spend $10,000,000 on
assets and the marketing team is expecting that after-tax operating cash flows in the first year
will total $1,000,000 and increase thereafter at 10% per year until the project ends in year 15.
The firm will sell-off all remaining assets, which are expected to have a salvage value of $100,000
at the end of the project. The firm will need to invest $500,000 in net working capital, of which it
expects to recover 50% at the end of the project. The appropriate discount rate is 11% and the
company is based in St. John's, NL where the corporate tax rate is 15%.
(a) Given the information above, would you recommend Dr. Cecilia Disney accept or reject
the project? Why or why not? (14 points)
𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝐶𝑜𝑠𝑡 = −10,000,000 − 500,000 = −10,500,000 [2 marks]
1,000,000 (1+10%) 15
𝑃𝑉 𝑂𝑝𝐶𝐹 = [1 − ((1+11%)) ] = 12,693,697.56 [3 marks]
11%−10%
((10,000,000−100,000)/15)∗15% 1
𝑃𝑉 𝐶𝐶𝐴 𝑇𝑆 = ∗ [1 − (1+11%)15 ] = 711,896.09 [4 marks]
11%
100,000+500,000∗50%
𝑃𝑉 𝐸𝑛𝑑 𝐶𝐹 = (1+11%)15
= 73,151.52 [2 marks]
NPV of Project = -10,500,000 + 12,693,697.56 + 711,896.09 + 73,151.52 = 2,978,745.16
You would recommend this project since the NPV is positive.
(b) Dr. Disney wants to know about the risk of the project, and asks you calculate the
breakeven point with respect to after-tax operating cash flows. What do you tell her the
maximum fall in after-tax cash flows can be in year 1 before the project’s NPV becomes
negative? (6 points)
Set NPV = 0
PV OPCF = Initial Cost – PV CCA TS – PV ECF
Solve for “C” in PV OPCF
2
Long and Short Answers
Question 1
A company is considering replacing some old equipment. The current market price of the old
equipment is $500,000 and the salvage value of the old equipment at the end of five years is
$150,000. The new equipment will cost $1,000,000 and could be sold at the end of five years
for $350,000. The new equipment requires an additional $40,000 of working capital which will
be released at the end of five years.
The new equipment is estimated to generate $500,000 in before-tax operating income in the
first year, compared with $300,000 for the old equipment. After the first year, these before tax
operating income amounts for both the old and new equipment would grow by 3% per annum.
Assume the tax rate is 40% and the discount rate is 10%. The old machine was purchased for
$1,000,000 five years ago.
Required:
a) (9 points)
Estimate the NPV of the replacement decision assuming that the asset class will remain
open and have a positive balance at the end of the five years.
a)
Δ Initial Cost = -1,000,000 – 40,000 + 500,000 = -540,000
Δ Pre-tax Operating Income = 500,000 – 300,000 = 200,000
Δ CCA per year = 130,000 – 85,000 = 45,000 [old machine depreciates by $850,000 over 10
years, the new machine by $650,000 over 5 years]
Δ Salvage Value at time 5 = 350,000 – 150,000 = 200,000
∆𝑃𝑉𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝐶𝑜𝑠𝑡 = −540,000
200,000(1 − 40%) 1 + 3% 5
∆𝑃𝑉𝑂𝑃𝐶𝐹 = [1 − ( ) ] = 480,312.01
10% − 3% 1 + 10%
45,000 ∗ 40% 1
∆𝑃𝑉𝑃𝑉 𝐶𝐶𝐴 𝑇𝑆 = [1 − ] = 68,234.16
10% (1 + 10%)5
200,000 + 40,000
∆𝑃𝑉𝐸𝐶𝐹 = = 149,021.12
(1 + 10%)5
∆𝑁𝑃𝑉𝑅𝑒𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 = −540,000 + 480,312.01 + 68,234.16 + 149,021.12 = 157,567.29
The NPV for replacement is positive, therefore the firm should replace the equipment.
1
, Question 2
The Chief Biomechanical Engineer (CBE) of a biotech startup company, Dr. Cecilia Disney, has
hired you as a consultant to evaluate a project. The engineering team and Dr. Disney are planning
to develop a new drug that may cure cancer. The company is expecting to spend $10,000,000 on
assets and the marketing team is expecting that after-tax operating cash flows in the first year
will total $1,000,000 and increase thereafter at 10% per year until the project ends in year 15.
The firm will sell-off all remaining assets, which are expected to have a salvage value of $100,000
at the end of the project. The firm will need to invest $500,000 in net working capital, of which it
expects to recover 50% at the end of the project. The appropriate discount rate is 11% and the
company is based in St. John's, NL where the corporate tax rate is 15%.
(a) Given the information above, would you recommend Dr. Cecilia Disney accept or reject
the project? Why or why not? (14 points)
𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝐶𝑜𝑠𝑡 = −10,000,000 − 500,000 = −10,500,000 [2 marks]
1,000,000 (1+10%) 15
𝑃𝑉 𝑂𝑝𝐶𝐹 = [1 − ((1+11%)) ] = 12,693,697.56 [3 marks]
11%−10%
((10,000,000−100,000)/15)∗15% 1
𝑃𝑉 𝐶𝐶𝐴 𝑇𝑆 = ∗ [1 − (1+11%)15 ] = 711,896.09 [4 marks]
11%
100,000+500,000∗50%
𝑃𝑉 𝐸𝑛𝑑 𝐶𝐹 = (1+11%)15
= 73,151.52 [2 marks]
NPV of Project = -10,500,000 + 12,693,697.56 + 711,896.09 + 73,151.52 = 2,978,745.16
You would recommend this project since the NPV is positive.
(b) Dr. Disney wants to know about the risk of the project, and asks you calculate the
breakeven point with respect to after-tax operating cash flows. What do you tell her the
maximum fall in after-tax cash flows can be in year 1 before the project’s NPV becomes
negative? (6 points)
Set NPV = 0
PV OPCF = Initial Cost – PV CCA TS – PV ECF
Solve for “C” in PV OPCF
2
