1. Last Study Topics Calculations of NPV & ROR
Managers and the Interests of Shareholders
Fundamental Study Result
Valuing Long-Lived Assets

2. Topics Covered PV Calculation Short Cuts Numeric Examples
How To Value Common Stock
Capitalization Rates

3. Instructor: Mr. Wajid Shakeel Ahmed
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

4. Instructor: Mr. Wajid Shakeel Ahmed
Short Cuts
Perpetuity - Financial concept in which a cash flow is theoretically received forever.
11/16/2014
Instructor: Mr. Wajid Shakeel Ahmed

5. Instructor: Mr. Wajid Shakeel Ahmed
Short Cuts
Perpetuity - Financial concept in which a cash flow is theoretically received forever.
11/16/2014
Instructor: Mr. Wajid Shakeel Ahmed

6. Instructor: Mr. Wajid Shakeel Ahmed
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
= $
11/16/2014
Instructor: Mr. Wajid Shakeel Ahmed

7. Instructor: Mr. Wajid Shakeel Ahmed
Short Cuts
Annuity - An asset that pays a fixed sum each year for a specified number of years.
11/16/2014
Instructor: Mr. Wajid Shakeel Ahmed

8. Instructor: Mr. Wajid Shakeel Ahmed
Case: leasing a car
Example
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

9. Instructor: Mr. Wajid Shakeel Ahmed
Continue
Example - 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?
11/16/2014
Instructor: Mr. Wajid Shakeel Ahmed

10. Instructor: Mr. Wajid Shakeel Ahmed
Case: Endowment Funds
Example - 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%?
11/16/2014
Instructor: Mr. Wajid Shakeel Ahmed

11. Instructor: Mr. Wajid Shakeel Ahmed
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 Multiply by $100,000, and we have our answer,
$851,400.
11/16/2014
Instructor: Mr. Wajid Shakeel Ahmed

12. Instructor: Mr. Wajid Shakeel Ahmed
11/16/2014
Instructor: Mr. Wajid Shakeel Ahmed

13. Instructor: Mr. Wajid Shakeel Ahmed
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

14. 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).

16. Continue
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 with the given amount in $;
PV = $100 x = $ 90.50

17. Continue
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 with the given amount in $;
PV = $100 x = $ 29.50

18. Continue
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 with the given amount in $;
PV = $100 x = $ 3.50

19. 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 , & with the given amount in $ and then add all the three resulted values;
PV1 = $100 x = $ 89.30
PV2 = $100 x = $ 79.70
PV3 = $100 x = $ 71.20
PV1 + PV2+ PV3 = $ $ $71.20 = $240.20

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)

21. Continue We can re – write it; After solving; 1 / 1 + r1 = 0.88

22. Continue 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

23. Continue Example: Annuity Factor Solution: After Solving;
AF2 = DF1 + DF2
After Solving;
AF2 = 1.70

24. Continue 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

25. 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?

26. Continue
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 with $ amount;
PV = $170,000 x = $886,720
NPV = PV - Investment
= $86,720

27. Continue
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
PV = $170,000 x
PV = $583,610

28. 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?

29. Continue Solution: a And, r Let St = salary in year t

30. Continue
Applying the annuity Formula;

31. Continue
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

32. 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?

33. 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.

34. 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

35. Continue
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 × [ ] = -$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

36. Continue
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

37. Summary PV Calculation Short Cuts Numeric Examples
How To Value Common Stock
Capitalization Rates