Perucho, Evrian E.
EE -3108
18-56299
Exercise no. 1
Financing with bonds
Problem no. 1
A corporation sold an issue of 20-year bonds, having a total face value of P10,000,000 for P9,500,000.
The bonds bear interest at 16%, payable semiannually. The company wishes to establish a sinking fund for retiring
the bond issue and will make semiannual deposit that will earn 12%, compounded semiannually. Compute annual
cost for interest and redemption of this bonds.
Given:
F= P10,000,000
r= 16%=0.16
i= 12%=0.12
since it is payable semi-annually
compounded semi-annually
r= 0.16/2 = 0.08
i= 0.12/2 = 0.06
Required:
1. annual cost for interest and redemption of this bonds.
Solution:
Compute for the Interest on the bond per period using the annual basis (16%), I
𝑰 = 𝑭𝒓
𝑰 = (𝑷𝟏𝟎, 𝟎𝟎𝟎, 𝟎𝟎𝟎)(𝟎. 𝟏𝟔)
𝑰 = 𝑷𝟏, 𝟔𝟎𝟎, 𝟎𝟎𝟎
Cash Flow Diagram
P 10,000,000
P 1,600,000
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
P
Compute for the periodic deposit for the sinking fund, A
𝑨=
𝑭
𝑭
𝑨 , 𝒊%, 𝒏
Where:
i= 0.06
n=20x2=40
𝑨=
𝑷𝟏𝟎, 𝟎𝟎𝟎, 𝟎𝟎𝟎
𝟏. 𝟎𝟔𝟒𝟎 − 𝟏
𝟎. 𝟎𝟔
𝑨 = 𝑷𝟔𝟒, 𝟔𝟏𝟓. 𝟑𝟓𝟗𝟐𝟏
Annual Expenses
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Compute for the total periodic expenses, (A+I) since the periodic deposit is compounded semiannually, the
formula will become, (2A+I).
𝒕𝒐𝒕𝒂𝒍 𝒑𝒆𝒓𝒊𝒐𝒅𝒊𝒄 𝒆𝒙𝒑𝒆𝒏𝒔𝒆𝒔 = 𝒕𝒐𝒕𝒂𝒍 𝒂𝒏𝒏𝒖𝒂𝒍 𝒆𝒙𝒑𝒆𝒏𝒔𝒆𝒔
𝒕𝒐𝒕𝒂𝒍 𝒑𝒆𝒓𝒊𝒐𝒅𝒊𝒄 𝒆𝒙𝒑𝒆𝒏𝒔𝒆𝒔 = 𝟐𝑨 + 𝑰
𝒕𝒐𝒕𝒂𝒍 𝒑𝒆𝒓𝒊𝒐𝒅𝒊𝒄 𝒆𝒙𝒑𝒆𝒏𝒔𝒆𝒔 = [𝟐(𝑷𝟔𝟒, 𝟔𝟏𝟓. 𝟑𝟓𝟗𝟐𝟏) + 𝑷𝟏, 𝟔𝟎𝟎, 𝟎𝟎𝟎]
𝒕𝒐𝒕𝒂𝒍 𝒑𝒆𝒓𝒊𝒐𝒅𝒊𝒄 𝒆𝒙𝒑𝒆𝒏𝒔𝒆𝒔 = 𝑷𝟏, 𝟕𝟐𝟗, 𝟐𝟑𝟎. 𝟕𝟏𝟖
P1,729,230.718 is the annual cost for interest and redemption of the bonds.
Perucho, Evrian E.
EE -3108
18-56299
Exercise no. 1
Financing with bonds
Problem no. 2
A company has issued 10-year bonds, with face value of P 1,000,000, in P1,000 units. Interest at 16% is
paid quarterly. If an investor desires to earn 20% nominal interest on P100,000 worth of these bonds, what
would the selling price have to be?
Given:
C= P1,000,000
F= P1,000,000/10 = P100,000
r= 16%=0.16
i= 20%=0.20
since it is paid quarterly
paid quarterly
r= 0.16/4 = 0.04
i= 0.20/4 = 0.0.05
Required:
1. selling price, P
Solution:
Compute for the Interest on the bond per period. (0.04)
𝑰 = 𝑭𝒓
𝑰 = (𝑷𝟏𝟎𝟎, 𝟎𝟎𝟎)(𝟎. 𝟎𝟒)
𝑰 = 𝑷𝟒𝟎𝟎𝟎
Cash Flow Diagram
P 100,000
P 4000
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
39 40
P
𝑷 = 𝑭𝒓 [
𝟏 − (𝟏 + 𝒊)−𝒏
] + 𝑪(𝟏 + 𝒊)−𝒏
𝒊
𝟏 − (𝟏 + 𝟎. 𝟎𝟓)−𝟒𝟎
𝑷 = (𝑷𝟏𝟎𝟎, 𝟎𝟎𝟎)(𝟎. 𝟎𝟒) [
] + 𝑷𝟏𝟎𝟎, 𝟎𝟎𝟎(𝟏 + 𝟎. 𝟎𝟓)−𝟒𝟎
𝟎. 𝟎𝟓
𝑷 = 𝑷𝟖𝟐, 𝟖𝟒𝟎. 𝟗𝟏𝟑𝟔𝟓
P82,840.91365 is the selling price at 20% nominal interest.
Perucho, Evrian E.
EE -3108
18-56299
Exercise no. 1
Financing with bonds
Problem no. 3
A P1,500-bond which will mature in 10 years and with a bond rate of 15% payable annually is to be
redeemed at par at the end of this period. If it is sold now for P1390, determine the yield at this price.
Given:
Required:
C=1500 =F
1. Yield at price of P1390
P= P1390
r= 15% = 0.15
Solution:
Compute for the Interest on the bond per period (0.15)
𝑰 = 𝑭𝒓
𝑰 = 𝑷𝟏𝟓𝟎𝟎(𝟎. 𝟏𝟓)
P1500.00
𝑰 = 𝑷𝟐𝟐𝟓
P225.00
0
1
2
3
4
5
6
P1390.00
𝑷 = 𝑭𝒓 [
𝟏 − (𝟏 + 𝒊)−𝒏
] + 𝑪(𝟏 + 𝒊)−𝒏
𝒊
𝑷𝟏𝟑𝟗𝟎 = 𝟏𝟓𝟎𝟎(𝟎. 𝟏𝟓) [
𝟏−(𝟏+𝒊)−𝟏𝟎
𝒊
] + 𝟏𝟓𝟎𝟎(𝟏 + 𝒊)−𝟏𝟎
𝒊 = 𝟎. 𝟏𝟔𝟓𝟒𝟖𝟑𝟔𝟕𝟒𝟗
𝒊 = 𝟏𝟔. 𝟓𝟓%
16.55% is the yield or interest rate at the price of P1390.
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