Question

Hi there, I have problem-solving this question, would definitely need help to explain if we need to look for the taxable income portion:

Question:

Topless:- A sporty convertible with a cost of $100,000 and a useful life of 5 years. It will produce rental income of $60,000 per year and operating costs of $10,000 per year. A major service is required after 3 years costing $15,000. A salvage value of $25,000 is expected after 5 Years. The required return is 10%.

Canopy:- A rugged off road vehicle costing $150,000 but with an expected useful life of only 3 years, due to the harsh conditions. It will produce rental income of $100,000 per year and operating costs of $20,000 per year. A major service is required after 2 years costing $10,000. A salvage value of $50,000 is expected after 3 Years. The required rate of return is 12%.

Income tax can be ignored.

Below are my calculations and explanation:

Topless
Cost	100,000
Required Return Rate	10.00%
life	5
Salvage Value	25,000
Operating Expenses (Per Year)	10000
Major Service (After 3rd year)	15,000
Annual Revenue	60,000
Topless
Relevant Cash Flow	0	1	2	3	4	5
Outlay	-100,000
Major Service					-15,000
Operating Expenditure		-10000	-10000	-10000	-10000	-10000
Cash Inflow		60,000	60,000	60,000	60,000	60,000
Salvage Value						25,000
Net Cash Flow Before Tax	-100,000	50000	50000	50000	35,000	75000
Net Cash Flow Before Tax (in Present Value)	-100,000	45454.5455	41322.31	37565.74	23905.47	46569.1
NPV	$94,817.17		PVIFA	3.790787
NPV	$ 94,817.17

23 24 Canop 25 Cost 26 Required Return Rate 27 life 28 Salvage Value 29 Operating Expenses (Per Year) 30 Major Service (After 2nd year) 31 Annual Revenue 32 33 Relevant Cash Flow 34 Outlay 35 Major Service 36 Operating Expenditure 37 Cash Inflow 38 Salvage Value 39 Net Cash Flow Before Tax 40 Net Cash Flow Before Tax (in Present Value 150,000 1 2 .00% 50,000 20000 10,000 100,000 In this project, we are using Perpetuity Chain because both of them are mutually exclusive and have different discount rate. Also, since both having positive NPV and we can only pick one for mutually exclusive project, we would do further analysis with Annual equivalent and Perpetuity Chain. If we are analysing based on Annual Equivalent, we would choose Topless.However, regarding of different discount rate, it reflects the uncertainty of the return and both have different risk. 150,000 10,000 2000020000-20000 100,000 100,000 100,000 50,000 80000 8000080000 150,000 71428.5714 63775.51 56942.42 With perpetuity chain formula, we get to see the value of the option in infinity. In perpetuity formula, it shows that topless brings higher return as compared to canopy. Hence, topless is the choice for this invesment. 150,000 $42,146.50 $42,146.50 42 NPV with excel formula 43 NPV with PV 2.401831 45 46 47 Annual Equivalent 48 Perpetuity Chain 49 Topless Canop 25,012.53 $17,547.65 $250,125.31 $146,230.44

Questions:

1. The NPV’s of the two cars.
2. An analysis of the two cars assuming they are mutually exclusive and can be repeated indefinitely.

Answer 1

Book1 Excel HOME INSERT PAGE LAYOUTFORMULAS DATA REVIEW VIEW ACROBAT KPMG S Cut Ee Copy Σ AutoSum -A Wrap Tot Calibri 恒桓茁Merge & Center. $. % ,留1: conditional Format as Cell Formatting TableStyles Paste Insert Delete Format Sort & Find& Filter Select B 1 u .田·ク· · Clear Format Painter Editing Font Cells Alignment C18 H I Topless Yr 2 Canopy Yr 1 Yr 3 Yr 4 Yr 5 Yr 2 Yr3 Yr 0 4 Initial Outflow 100000.0 itial Outflow 5 Operating Income 60000.00 60000.0060000.0060000.00 60000.00 10000.00 -10000.00-10000.00-10000.00 Income 100000 100000 100000 7 Major Service Cost 15000.00 Major Service Cost 10000 25000.00 value Total PVF @10% Present value NPV 9 Total 10PVF @ 10% 11 Present value 12 NPV 13 PVAF 14 Annual Equivalent NP 100000.00 50000.00 0.9091 50000.00 50000.00 35000.0075000.00 150000.00 80000.0080000.00120000.00 1 0.892857143 0.797193878 0.711780248 1.0000 100000.00 45454.551 0.6830 0.6209 551 41322.31| 37565.74| 23905.47| 46569.10 0.8264 0.7513 150000.00 71428.5763775.5 94817.17 70617.71 2.401 25012.53 250125.31 Annual Equivalent NP 29401.61 al Chain al Chairn 294016.12 17 18 20 21 Sheet1 + 100% 05:03 PM ^ 마. x 04/19/19 O Type here to search

Formula View:

Book1-Excel HOME INSERT PAGE LAYOUT FORMULASI DATA REVIEW VIEW ACROBAT KPMG Ashow Formulas <pError Checking. . (S Evaluate Formula Define Name % Use in Formula Trace precedents 嚷Trace Dependents Remove Arrows Calculate Now watch Calculation Calculate Sheet nsert AtoSum Recently Financial Logical Text Date &Lookup &Math & More Name Create from Selection Defined Names Function Time-Reference. Tng. Functions. Used- Manager Window Options. Function Library Formula Auditing C18 Topless Yr 2 Canopy Yr 0 4 Initial Outflow 100000 nitial Outflow Operating Operating Expenditure Major Service Cost Salvage value Total PVF 10% Present value NPV 5 Operating Income 60000 60000 60000 10000 60000 10000 15000 60000 10000 Income 100000 100000 100000 Operating Expenditure 7 10000 10000 Major Service Cost 10000 value 9 Total 10PVF @ 10% 11 Present value 12 NPV 13 PVAF C10/1.1-D10/1.1- -D10 D9 -E10/1.1 -F10/1.1 -G10 G9 :1/1.12 し10/1.12 |:M10/1.12 -N10N9 9 -810 B9 -SUM(B11:G11) -SUM(C10:G10) -C10 C9 E10 E9 -K10 K9 SUM(K11:N11) -SUM(L10:N10) Annual Equivalent NPV-B12/B13 Perpetual Chain nual Equivalent NPV-K12/K13 -K14/0.1 -B14/0.1 tual Chain 18l 20 Sheetl + 100% 05:04 PM ^ 마. x 04/19/19 O Type here to search

Answer: Whenever, useful life of two projects are different then we have to calculate Equivalent Annual NPV. In the given question, Overall NPV of Topless is higher since it has useful life of 5 years. But after calculating Equivalent Annual NPV Canopy is found more profitable than Topless in terms of both Perpetual Annuity as well as Annual NPV.

Note: In your analysis of "canopy" Salvage value has not considered. That's why answer for canopy is different and it has also impact on final answer.

If you have any Queries/Suggestions, feel free to ask me in the comment box.