Financial Management – Assignment
Asfa Asfia [18102002]
AS B 18 IP
1.
2.
3.
4.
5.
What is bond? 5 point
What is stock? 5 point
What difference between zero coupon bond and coupon bond? 5 point
What difference between NPV, IRR, and PI? 5 point
The yield to maturity of a $1000 bond with 7% coupon rate, semiannual coupon coupons,
and two years to maturity is 7.6% APR, compounded semiannually. What must its price
be? 10 point
6. Bond X is a premium bond making annual payments. The bond pays an 8 percent coupon,
has a YTM of 6 percent, and has 13 years to maturity. Bond Y is a discount bond making
annual payments. This bond pays a 6 percent coupon, has a YTM of 8 percent, and also
has 13 years to maturity. If interest rates remain unchanged, what do you expect the price
of these bonds to be one year from now? In three years? In eight years? In 12 years? In 13
years? What’s going on here? Illustrate your answers by graphing bond prices versus time
to maturity? 15 point
7.
If you own 18,000 shares of stock of Nike and it pays a dividend of $0.35 per share, then
the price when buy these stocks in 2015 was $18 per share, now the price $20 per share.
What is total profit if you sell all your Nike shares now? 15 point
8.
Summit systems will pay a dividend of $2.5 this year. If you expect Summit dividend to
grow by 4% per year, what is its price per share if the firm equity cost of capital is 9%?
10 point
9.
You have been offered a unique investment opportunity. If you invest $10,000 today, you
will receive $500 one year from now, $1500 two year from now, and $10,000 three years
from now.
a.
What is the NPV of the opportunity if the cost of capital is 6% per year? Should you
take the opportunity? 10 point
b.
What is the IRR? Bonus ++
c.
How long is the profitability index? 10 point
10.
For the cash flows below, suppose the firm uses the NPV decision rule. At a required return
of 11 percent, should the firm accept this project? What if the required return was 30 percent?
10 point
Year
0
1
2
3
Cash Flow
-$34,000
16,000
18,000
15,000
Answer
1. Bond is a security sold by governments and corporations to raise money from investors
today in exchange for a promised future payment. A bond is normally an interest-only loan,
meaning that the borrower will pay the interest every period, but none of the principal will
be repaid until the end of the loan.
2. Stock is a security that represents the ownership of a fraction of a corporation. This entitles
the owner of the stock to a proportion of the corporation's assets and profits equal to how
much stock they own.
3. The difference between zero-coupon bond and coupon (regular) bond
a. The zero-coupon bond pays bondholders interest, while the coupon bond does not issue
such interest payments, otherwise known as coupons. Instead, zero-coupon
bondholders merely receive the face value of the bond when it reaches maturity, while
coupon paying bondholders receive both the face value, while also receiving coupons,
over the life of the bond.
b. Zero-coupon bondholders gain on the difference between the price they pay for the
bond and the amount they will receive at the bond's maturity. This can be substantial,
because zero-coupon bonds are typically purchased at drastically reduced prices,
known as deep discounts, to the bond’s face value. In other words, a zero-coupon
bondholder derive financial gain from the difference between the bond’s purchase
price and its face value, while the coupon bondholders profit from the regular
distribution of interest payments.
c. Coupon bonds pay bondholders interest payments throughout the lives of the bonds,
while zero-coupon bonds do not issue such interest payments, which are otherwise
known as coupons.
d. Coupon bonds, however, provide regular interest payments to the bondholder, and at
maturity, the bondholder receives the face value of the bond. That can seem to be a
bigger advantage, but practically, the yield of zero coupon bonds is usually higher than
ordinary bonds.
4. The difference between between NPV, IRR, and PI
Point of difference
Net Present
Internal Rate of
Value (NPV)
Return (IRR)
Meaning
The difference
The interest rate
between the
that sets the net
present value of a present value of the
project’s or
cash flows
investment’s
equal to zero.
benefits and the
present
value of its costs.
Profitability Index
The ratio of the
present value of a
project’s future net
cash flows to the
projet’s initial cash
outflow
Expressed as
We express NPV IRR is expressed in PI is expressed in
in the form of the
form
of the form of a ratio
currency returns. percentage returns.
Focus
NPV focuses on
determining
whether
the
investment
is
generating surplus
returns than the
expected returns.
IRR focuses on
determining what is
the breakeven rate
at which the present
value of the future
cash flows becomes
zero.
Discount Rate
NPV requires the
use of a discount
rate which can be
difficult
to
ascertain.
IRR doesn’t have PI uses a discount
this difficulty since rate to discount the
it ‘calculates’ the future cash flows.
rate of return.
Calculation of
Present Value
NPV calculates IRR ignores the
the present value present value of
of future cash future cash flows.
flows.
5. Information given :
Face Value = $1000
Coupon rate = 7%, semiannual coupons
Maturity
= 2 years
y
= 7.6% APR is equal to semiannual rate 3.8%
CPN =
CPN =
Coupon Rate x Face Value
Number of Coupon Payments per Year
0.07 x 1000
2
CPN = $35
Thus, the amount of coupon each payment is $35
1
1
𝐹𝑉
𝑃 = 𝐶𝑃𝑁 × (1 −
)
+
(1 + 𝑦)𝑁
(1 + 𝑦)𝑁
𝑦
PI
focuses
on
determining how
many times of the
initial investment
are we going to get
back.
The PI method
calculates
the
present value of
future cash flows.
1
1
1000
𝑃 = 35 × 0.038 (1 − (1.038)2 ) + (1.038)2 = $994,33
Evaluate : Thus, the bond price must be $994,33
6. Information given :
Assume face value of bond $1000
Bond X premium, annual
Coupon rate = 8%
YTM
= 6%
Maturity
= 13 year
Bond Y discount, annual
Coupon rate = 6%
YTM
= 8%
Maturity
= 13 year
Manual Calculation :
X Corporation bond:
Annual coupon Payment for X Bond = $1000 x 8% = $80
P = C(PVIFAR%,t) + $1,000(PVIFR%,t)
P0
= $80(PVIFA3%,26) + $1,000(PVIF3%,26)
P1
= $80(PVIFA3%,24) + $1,000(PVIF3%,24)
P3
= $80(PVIFA3%,20) + $1,000(PVIF3%,20)
P8
= $80(PVIFA3%,10) + $1,000(PVIF3%,10)
P12 = $80(PVIFA3%,2) + $1,000(PVIF3%,2)
P13
= $1,171.05
= $1,167.68
= $1,124.20
= $1,053.46
= $1,018.87
= $1,000
Y Corporation bond:
Annual coupon Payment for X Bond = $1000 x 6% = $60
P0
P1
P3
P8
P12
P13
= $30(PVIFA4%,26) + $1,000(PVIF4%,26)
= $30(PVIFA4%,24) + $1,000(PVIF4%,24)
= $30(PVIFA4%,20) + $1,000(PVIF4%,20)
= $30(PVIFA4%,10) + $1,000(PVIF4%,10)
= $30(PVIFA4%,2) + $1,000(PVIF4%,2)
= $841.92
= $849.28
= $885.07
= $948.46
= $981.48
= $1,000
Excel Calculation :
X Corporation bond:
Annual coupon Payment for X Bond = $1000 x 8% = $80
P0
P1
P3
P8
P12
P13
Formula
PV(6%;0;-80;-1000)
PV(6%;1;-80;-1000)
PV(6%;3;-80;-1000)
PV(6%;8;-80;-1000)
PV(6%;12;-80;-1000)
PV(6%;13;-80;-1000)
Price
$1.000,00
$1.018,87
$1.053,46
$1.124,20
$1.167,68
$1.177,05
Y Corporation bond:
Annual coupon Payment for X Bond = $1000 x 6% = $60
P0
P1
P3
P8
P12
P13
Formula
PV(8%;0;-60;-1000)
PV(8%;1;-60;-1000)
PV(8%;3;-60;-1000)
PV(8%;8;-60;-1000)
PV(8%;12;-60;-1000)
PV(8%;13;-60;-1000)
Price
$1.000,00
$981,48
$948,46
$885,07
$849,28
$841,92
Graph :
Evaluate : All else held equal, the premium over par value for a premium bond declines as
maturity approaches, and the discount from par value for a discount bond declines as
maturity approaches. This is called “pull to par.” In both cases, the largest percentage price
changes occur at the shortest maturity lengths.
As the number of years are increasing, the value of bond X decreasing and the value of the
bond Y is increasing. The difference in the present values of bond X and bond Y is because
of the different coupon rates and yields.
For Bond X the coupon rate is greater than the yield which results in higher bond price and
for Bond Y the coupon rate is less than the yield which results in the lower bond price with
the increase in the number of years.
7. Information given :
Stocks
= 18,000
Dividen
= $0,35
Price in 2015 = $18
Current Price = $20
Total Return
Total profit = $20 - $18 = $2
Or equal to (18,000 x $20) - (18,000 x $18) = $36,000
Evaluate, Thus, total gain is $36,000
8.
Information given :
Div1 = $2.5
g
= 0.04
Cost of capital = 0.09
P0 =
Div1
rE−g
=
$2.5
0.09−0.04
= $50
Evaluate, Thus, the price per share is $50
9.
Solution 9.a
Information given :
NPV = -10,000 +
NPV = $202,89
500
(1+0.06)1
+
1,500
(1+0.06)2
+
10,000
(1+0.06)3
Evaluate : Since the NPV is positive we should take it.
Solution 9.b
IRR (internal rate of return) is The interest rate that sets the net present value of the cash
flows equal to zero.
Solution 9.c
Discounting the cash flow :
$500 / (1,06)
= $471,70
$1,500 / (1,06)2
= $1,335
3
$10,000 / (1.06)
= $8,396.20
= $10,202.9
Profitability index
= Present Value of Future Cash Flows/Initial Cash Flow
= $10,202.9 / $10,000
= 1,02
Evaluate : Since the PI 1.02 > 1 the company should proceed the project
10.
Information given :
Year
0
1
2
3
Cash Flow
-$34,000
16,000
18,000
15,000
Rate 11%
NPV
= -34,000 +
16,000
(1+0.11)1
+
18,000
(1+0.11)2
+
15,000
(1+0.11)3
= $5,991.49
Evaluate : Since the NPV is positive the project should be taken
Rate 30%
NPV = -34,000 +
16,000
(1+0.30)1
+
18,000
(1+0.30)2
+
15,000
(1+0.30)3
= -4,213.93
Evaluate : As the NPV is negative the project should not be taken