economics engineering CAPITAL FINANICING WITH BONDS

economic engineering BONDS

1. F = F + R
pd
P (1+i) =n[ ](1+i) -1d + R
n
i
P =
[ ](1+i) -1d +
n
i(1+i)n
R
(1+i)n
Bonds
- interest-bearing security which promises to pay
a stated amount of money on the maturity date1.
regular interest payment called coupons/dividends2.
face value - future value
coupon / dividend - annuity
fair price - present value
company
bank
investors
bonds
coupons / dividends
redemption value
utang
nagpautang
P = bond price
R = redemption price
i = interest rate / yield to maturity
n = maturity period
d = dividends / coupons
d = r F
<
F
<
r = bond rate
= face / par value
*
|
[ ](1+i) -1
|||||
0 1 2 3 4 5 n
d d d d d
bond|
d
Redemption value
F = P (1+i)
p
n
F = d
d
n
i
P

2. P =
[ ](1+i) -1d +
n
i(1+i)n
R
(1+i)n
P = bond price
R = redemption price
i = interest rate / yield to maturity
n = maturity period
d = dividends / coupons
d = r F
<
F
<
r = bond rate
= face / par value
*
A government bond makes an annual coupon payment of P4,500 and has a
redemption value of P50,000. The bond matures in 10 years. Determine
the price of this bond if the yield to maturity is 4% per annum.

3. P =
[ ](1+i) -1d +
n
i(1+i)n
R
(1+i)n
A corporation issues a bond with a 5% annual coupon rate. The bond has
a face value of P150,000 and matures in 10 years. What is the price of
this bond if the yield to maturity is currently 4.5%?
P = bond price
R = redemption price
i = interest rate / yield to maturity
n = maturity period
d = dividends / coupons
d = r F
<
F
<
r = bond rate
= face / par value
*

4. P =
[ ](1+i) -1d +
n
i(1+i)n
R
(1+i)n
A P100,000, 10% bond, pays dividend every quarter for 8 years. The bond
is priced at par and is redeemable at 110% of the par value. Find the
yield to maturity.
P = bond price
R = redemption price
i = interest rate / yield to maturity
n = maturity period
d = dividends / coupons
d = r F
<
F
<
r = bond rate
= face / par value
*

5. P =
[ ](1+i) -1d +
n
i(1+i)n
R
(1+i)n
A bond with a face value of P1,000,000 and is bearing an interest of 6%
per year payable semi-annually and due in 5 years. If you want to earn
8% semi-annually, how much are you willing to pay for the bond?
P = bond price
R = redemption price
i = interest rate / yield to maturity
n = maturity period
d = dividends / coupons
d = r F
<
F
<
r = bond rate
= face / par value
*

6. P =
[ ](1+i) -1d +
n
i(1+i)n
R
(1+i)n
P = bond price
R = redemption price
i = interest rate / yield to maturity
n = maturity period
d = dividends / coupons
d = r F
<
F
<
r = bond rate
= face / par value
*
What is the maximum among an investor should pay for a 25-year bond with a P20,000 face value
and 8% coupon rate (interest only paid semi-annually)? The bond will be kept to maturity. The
investor’s effective annual interest rate for economic decisions is 10%.

7. P =
[ ](1+i) -1d +
n
i(1+i)n
R
(1+i)n
P = bond price
R = redemption price
i = interest rate / yield to maturity
n = maturity period
d = dividends / coupons
d = r F
<
F
<
r = bond rate
= face / par value
*
A municipal bond with a face value of $10,000 will mature 15 years from now. The bond interest
rate is 6% per year, payable quarterly. At an interest rate of 16% per year compounded
quarterly, the present worth of the bond is closest to?

8. P =
[ ](1+i) -1d +
n
i(1+i)n
R
(1+i)n
P = bond price
R = redemption price
i = interest rate / yield to maturity
n = maturity period
d = dividends / coupons
d = r F
<
F
<
r = bond rate
= face / par value
*
Emily is saving for her retirement. She plans to deposit $500 at the end of
each month into an investment account that offers annual interest of 7%,
compounded monthly. If she plans to save for 25 years, how much will she have
saved up at the time of her retirement, assuming her target retirement fund
is $1,000,000?

9. P =
[ ](1+i) -1d +
n
i(1+i)n
R
(1+i)n
Sophia is planning to save up for a new car. She wants to deposit $400 at the end of each
month into an investment account that offers an annual interest rate of 3%, compounded
monthly. If she plans to save for 4 years, how much will she have saved up at the end of the
saving period, assuming her target car fund is $25,000?
P = bond price
R = redemption price
i = interest rate / yield to maturity
n = maturity period
d = dividends / coupons
d = r F
<
F
<
r = bond rate
= face / par value
*

10. P =
[ ](1+i) -1d +
n
i(1+i)n
R
(1+i)n
P = bond price
R = redemption price
i = interest rate / yield to maturity
n = maturity period
d = dividends / coupons
d = r F
<
F
<
r = bond rate
= face / par value
*
A bond is currently priced at P120,000. It pays an annual coupon of P5,000
and the yield to maturity is 6% per annum. The bond will mature in 15
years. Calculate the redemption value of this bond.

11. P =
[ ](1+i) -1d +
n
i(1+i)n
R
(1+i)n
P = bond price
R = redemption price
i = interest rate / yield to maturity
n = maturity period
d = dividends / coupons
d = r F
<
F
<
r = bond rate
= face / par value
*
A corporation issues a bond with an annual coupon rate of 6%. The bond matures in 5 years and pays
its coupon quarterly. The current market price of the bond is P98,000, and the yield to maturity is 7%
per annum, compounded quarterly. Calculate the Redemption Value (Face Value) of the bond.