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![Page 1: Last Study Topics Calculations of NPV & ROR Managers and the Interests of Shareholders Fundamental Study Result Valuing Long-Lived Assets.](https://reader031.fdocuments.us/reader031/viewer/2022032202/56649d6e5503460f94a4fb08/html5/thumbnails/1.jpg)
Last Study Topics
• Calculations of NPV & ROR• Managers and the Interests of Shareholders• Fundamental Study Result• Valuing Long-Lived Assets
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Topics Covered
• PV Calculation Short Cuts• Numeric Examples• How To Value Common Stock• Capitalization Rates
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Short Cuts
• Sometimes there are shortcuts that make it very easy to calculate the present value of an asset that pays off in different periods.
• These tolls allow us to cut through the calculations quickly.
11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed
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Short CutsPerpetuity - Financial concept in which a cash flow is theoretically received forever.
PV
Cr
cashflow
luepresent va
Return
11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed
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Short CutsPerpetuity - Financial concept in which a cash
flow is theoretically received forever.
r
CPV 1
ratediscount
flow cash FlowCash of PV
11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed
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Case : Investment A• An investment costs $1,548 and pays $138 in
perpetuity. If the interest rate is 9 percent, what is the PV of the perpetuity?
– PV = C / r = $1533.33
11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed
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Short CutsAnnuity - An asset that pays a fixed sum each
year for a specified number of years.
trrrC
1
11annuity of PV
11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed
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Case: leasing a carExample
You agree to lease a car for 4 years at $300 per month. You are not required to pay any money up front or at the end of your agreement. If your opportunity cost of capital is 0.5% per month, what is the cost of the lease?
11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed
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ContinueExample - continued
You agree to lease a car for 4 years at $300 per month. You are not required to pay any money up front or at the end of your agreement. If your opportunity cost of capital is 0.5% per month, what is the cost of the lease?
10.774,12$
005.1005.
1
005.
1300Cost Lease 48
Cost
11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed
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Case: Endowment FundsExample - Suppose, for example, that we begins to wonders what it would cost to contribute in a endowment fund with an amount of $100,000 a year for only 20 years, having opportunity cost of 10%?
400,851$
10.110.
1
10.
1000,100Cost Lease 20
Cost
11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed
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Alternatively• We can simply look up the answer in the annuity table given on the next slide. • This table gives the present value of a dollar to be received in each of t periods. • In our example t = 20 and the interest rate r = .10, and therefore;• We look at the twentieth number from the top in the 10 percent column. It is 8.514. Multiply 8.514 by $100,000, and we have our answer,$851,400.
11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed
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11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed
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Compound Interest
• There is an important distinction between compound interest and simple interest.– When money is invested at compound interest,
each interest payment is reinvested to earn more interest in subsequent periods.
– In contrast, the opportunity to earn interest on interest is not provided by an investment that pays only simple interest.
11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed
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Numericals
• Example: PV • Use the discount factors shown on to the next
slide to calculate the PV of $100 received in:– a. Year 10 (at a discount rate of 1 percent).– b. Year 10 (at a discount rate of 13 percent).– c. Year 15 (at a discount rate of 25 percent).– d. Each of years 1 through 3 (at a discount rate of
12 percent).
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• Solution: Year 10 (at a discount rate of 1 percent).
• A- PV of the $100 can be calculated through multiplying the discount factor i.e. 0.905 with the given amount in $;
• PV = $100 x .905 = $ 90.50
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• Solution: Year 10 (at a discount rate of 13 percent).
• A- PV of the $100 can be calculated through multiplying the discount factor i.e. 0.295 with the given amount in $;
• PV = $100 x .295 = $ 29.50
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• Solution: Year 15 (at a discount rate of 25 percent).
• A- PV of the $100 can be calculated through multiplying the discount factor i.e. 0.035 with the given amount in $;
• PV = $100 x .035 = $ 3.50
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Continue• Solution: Each of years 1 through 3 (at a discount rate of
12 percent).• A- PV of the $100 can be calculated through multiplying
the discount factors i.e. 0.893, 0.797 & 0.712 with the given amount in $ and then add all the three resulted values;
• PV1 = $100 x .893 = $ 89.30 • PV2 = $100 x .797 = $ 79.70• PV3 = $100 x .712 = $ 71.20
– PV1 + PV2+ PV3 = $89.30 + $79.70 + $71.20 = $240.20
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• Example: Interest rate• If the one-year discount factor is .88, what is
the one-year interest rate?• Solution:We know that; • DF1 = 1 / 1 + r1, Here; • DF1 = 0.88 (Given)
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• We can re – write it;
– 1 / 1 + r1 = 0.88
• After solving;– r1 = 13.6%
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• Example: Discount Factor• If the two-year interest rate is 10.5 percent,
what is the two-year discount factor?• Solution:– DF2 = 1 / (1 + r2)2
After Solving;– DF2 = 0.82
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• Example: Annuity Factor
• Solution:– AF2 = DF1 + DF2
• After Solving;– AF2 = 1.70
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• Example: 3 year – Annuity Factor• If the PV of $10 a year for three years is $24.49,
what is the three-year annuity factor?• solution:– PV of an annuity = C × [Annuity factor at r% for t
years]– $24.49 = $10 x [AF3]
• After Solving;– AF3 = 2.45
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Case: Factory
• Example: • A factory costs $800,000. You reckon that it
will produce an inflow, after operating costs, of $170,000 a year for 10 years. If the opportunity cost of capital is 14 percent;
– what is the net present value of the factory? What will the factory be worth at the end of five years?
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• Solution:• We need to calculate the PV of the 10-year
stream of Cash inflows, which is $ 170,000,• We multiply the discount factor (Using the Table)
i.e. 5.216 with $ amount;– PV = $170,000 x 5.216 = $886,720– NPV = PV - Investment
– = $86,720
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• In order to find the five years ended value of the factory will be the present value of the five remaining $170,000 cash flows times the discount factor i.e. 3.433.
– PV = $170,000 x 3.433– PV = $583,610
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Case: Harold Filbert• Harold Filbert is 30 years of age and his salary
next year will be $20,000. Harold forecasts that his salary will increase at a steady rate of 5 percent per annum until his retirement at age 60.
– a. If the discount rate is 8 percent, what is the PV of these future salary payments?
– b. If Harold saves 5 percent of his salary each year and invests these savings at an interest rate of 8 percent, how much will he have saved by age 60?
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• Solution: a– Let St = salary in year t– St = $20,000 / (1 + 5%) = $ 19,048
• And, r – r = (1 + 8%) / (1 + 5%)– r = (1 + .29%)– r = (1.029)
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• Applying the annuity Formula;
trrrC
1
11annuity of PV
222,378$
029.1029.
1
029.
1048,19$PV 30
PV
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• Solution: b
• The calculated PV of the salary is $378,222 and the saving amount can be calculated as under;– $ 378,222 x 5% = $18,911
• And, saving amount after 30 years would becomes;– Future Value = $18,911 X (1.08)30
= $ 190,295
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Case: Ship
• Halcyon Lines is considering the purchase of a new bulk carrier for $8 million. The forecasted revenues are $5 million a year and operating costs are $4 million. A major refit costing $2 million will be required after both the fifth and tenth years. After 15 years, the ship is expected to be sold for scrap at $1.5 million. If the discount rate is 8 percent, what is the ship’s NPV?
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• Solution:• We can break this down into several different
cash flows, such that the sum of these separate cash flows is the total cash flow.
• Then, the sum of the present values of the separate cash flows is the present value of the entire project. All dollar figures are in millions.
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Continue• Cost of the ship is $8 million• INV = -$8 million• Revenue is $5 million per year, operating
expenses are $4 million. • Thus, operating cash flow is $1 million per
year for 15 years.– PV = $1 million × [Annuity factor at 8%, t = 15] – = $1 million × 8.559 – PV = $8.559 million
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• Major refits cost $2 million each, and will occur at times t = 5 and t = 10.– PV = -$2 million × [Discount factor at 8%, t = 5]– PV = -$2 million × [Discount factor at 8%, t = 10]– PV = -$2 million × [0.681 + 0.463] = -$2.288 million
• Sale for scrap brings in revenue of $1.5 million at t = 15.– PV = $1.5 million × [Discount factor at 8%, t = 15]– PV = $1.5 million × [0.315] = $0.473
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• Adding these present values gives the present value of the entire project:
– PV = -$8 million + $8.559 million - $2.288 million + $0.473 million
• PV = -$1.256 million
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Summary
• PV Calculation Short Cuts• Numeric Examples• How To Value Common Stock• Capitalization Rates