# Internal Rate of Return by xiuliliaofz

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```									Internal Rate of Return

The IRR is a rate of return calculation that equates the PRESENT value of the cash inflows (both
dividends and selling price) with the present value of the cash outflows (cost of the investment). It is
computed the same as yield to maturity on a bond and is also referred to as the DOLLAR weighted
rate of return.
NOTE: It assumes all cash flows are reinvested at the IRR rate.

A. Identify the keystrokes on the HP-1OBII used to compute IRR.
CFj , Shift, Nj , IRR, NPV

B. Examples:
1. Compute the market price on a 10% twenty year \$1,000 bond that pays interest
semiannually.
Comparable bonds are yielding 12%.

10B(II): O CFj, 50 CFj, 39 ,█, Nj, 1050 CFj, 6 I/YR, █, NPV = 849.54

2. A client invests \$50,000 for property that could be sold five years later for \$150,000.
Assume the net cash flow for each of the next five years is as follows:
Year 1: -\$20,000                 Year 3:      0            Year 5: +\$20,000
Year 2: -\$10,000                 Year 4: +\$15,000

Compute the IRR assuming that all cash flows occur at the end of the year.

10B(II): 50000, +/-, CFj, 20000, +/-, CFj, 10000, +/-, CFj, O, CFj, 15000, CFj,
170000, CFj, █, IRR/YR = 20.69%

Net Present Value (NPV)

3. A client purchased land on January 1 and made \$20,000 of improvements that were
paid for at the end of year 1. The land was not rented until year 5 when at the end of
the year she received \$25,000 in rent and sold the land for \$175,000. Compute the
purchase price of the land assuming she earned a 12% return on her investment.

10b(II):            O, CFj, 20000, +/-, CFj, O, CFj, 3, █, Nj, 200000, CFj, 12, I/YR,
█, NPV = 95,628.23

Identify the formula for the inflation adjusted rate of return.

1 + Interest rate - 1 x 100
1 + Inflation rate
C. Example: Assume an investment produces a twelve percent rate of return when
inflation is five percent. Compute the inflation adjusted rate of return.

Step #1              Step #2        Step # 3
(1 +.12)      -     1          x   100       =   6.67 %
(1 +.05)                                           NOTE: Inflation adjusted return will
always fall between rate of return and
inflation.

.12        . .667
667      .05
Bonds
1. List the four factors used to determine a bond’s price.

1. Coupon interest rate    2. Market interest rate     3. Maturity Value     4. Principal
(PMT key)                 (I/YR key)                  (FV key)             (PV key)

A. Describe the procedure for computing the price of a bond.
Compute the present value of the future cash inflows using the market rate of interest for similar
debt. For example, the price of a \$1,000 bond that has a coupon rate of 7% and pays interest
semi-annually that will mature in ten years assuming comparable bonds are yielding 8% is
\$932.05. If similar bonds are yielding 6% the price would be 1,074.39.

8%: n= 20       i= 8/2    PMT= 35         FV= 1,000        PV= -932.05
6%: n= 20       i= 6/2    PMT= 35         FV= 1,000        PV= -1,074.39

B. Explain the difference between bonds selling at a “discount” versus “premium.”
1. Discount
A bond selling at a discount means that it is selling for LESS than its face value
because its coupon rate is lower than the market rate. By selling it at a discount the
yield can be EQUATED to the market rate for similar debt.
A bond selling at a premium means that it is selling for MORE than its face value
because its coupon rate is higher than the market rate. Similar to a discount, this
premium equates the YIELD to the market rate for similar debt.

C. Explain each of the following bond yields.
1. Current yield
The current yield refers to the annual income from a bond’s coupon payments divided by
its current MARKET price. The annual income is fixed, but the current market price of
the bond changes with interest rates.

Current Yield = Current coupon payments
Current market price
Example:
Compute the current yield for a \$1,000 bond with a coupon rate of 8% that is currently
selling for \$925. Also, if the bond was selling for \$1,060.

\$80/\$925 = 8.65%                 \$80/\$1,060 = 7.55%

2. Yield to Maturity
Yield to maturity is the rate of return earned on a bond from the time of purchase until it
matures or is sold. It includes BOTH the interest payments and gain or loss on
disposition and assumes interest payments are reinvested at the yield to maturity rate.
Example:
A twenty year 8% bond that pays interest semiannually is selling for \$699.07. Compute
the bonds yield to maturity.

n = 40       FV = 1,000      PV = -699.07       PMT = 40         i = 12%
(6 x 2 = annual rate)
3. Yield to call
Yield to call is the return earned on a bond from its purchase date to its call date. It is
computed exactly the same as yield to MATURITY except the call date is substituted for
the maturity date and the call price for the maturity price.

Example: “X” Company issues a twenty year 7% bond that pays interest semiannually for its
par value. “X” has the option to call the bond in five years for 110% of its face value.
Compute the yield to call.
n = 10      FV = 1,100      PV = -1,000       PMT = 35        i = 8.64%
(4.32 x 2 = annual rate)

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