last study topics calculations of npv & ror managers and the interests of shareholders...

Last Study Topics

• Calculations of NPV & ROR• Managers and the Interests of Shareholders• Fundamental Study Result• Valuing Long-Lived Assets

Topics Covered

• PV Calculation Short Cuts• Numeric Examples• How To Value Common Stock• Capitalization Rates

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

Short CutsPerpetuity - Financial concept in which a cash flow is theoretically received forever.

PV

Cr

cashflow

luepresent va

Return


Short CutsPerpetuity - Financial concept in which a cash

flow is theoretically received forever.

r

CPV 1

ratediscount

flow cash FlowCash of PV


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


Short CutsAnnuity - An asset that pays a fixed sum each

year for a specified number of years.

trrrC

1

11annuity of PV


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?


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


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


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.


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.


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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• PV = $100 x .295 = $ 29.50

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• PV = $100 x .035 = $ 3.50

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

Continue

• 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

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

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)

Continue

• 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

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?

Continue

• 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.

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

Summary

• PV Calculation Short Cuts• Numeric Examples• How To Value Common Stock• Capitalization Rates

last study topics calculations of npv & ror managers and the interests of shareholders...

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