1. How much would you be willing to pay for a bond that pays semi-annual coupon
ID: 2754283 • Letter: 1
Question
1. How much would you be willing to pay for a bond that pays semi-annual coupon payments and has the following characteristics: (a) NPER: 12, (b) YTM: 5.25%, and Coupon Payment: $25.80.
2. What is the maximum price that you would be willing to pay for a non-constant growth stock that has the following characteristics: (a) Non-Constant Growth Rate: 20%, (b) Constant Growth Rate: 5.5%, (c) Dividend: $2.36, and (d) Required Rate of Return: 12%.
3. Calculate the difference between daily and annual compounding, given the following information: (a) PV: $25,000, (b) NPER: 30, and (c) RATE: 11%.
4. Calculate the PMT on a mortgage, given the following information: (a) PV: $362,000, (b) RATE: 5%, and NPER: 30.
5. Calculate the RATE given the following characteristics: (a) PMT: $15,250 (you are paying), (b) FV: $134,000, and (c) NPER: 10.
6. Calculate the required rate of return on a company’s stock that has the following characteristics: (a) Constant Growth Rate: 4%, (b) Price: $22.30, and (c) Dividend (Has Been Paid): $5.00.
Explanation / Answer
(‘1) Bond Price
P = C/YTM x [1-(1+YTM)-n] + FV (1+YTM)-n
Where C= 25.80,
YTM = 5.25/2 = 2.63 ( Semi annual YTM)
‘n = 12
FV = 1000
By putting the values in formula we get
P = 25.80/.263 x [1-(1.0263)-12] + 1000 (1.0263)-12
P = 1627.36
Maximum price can be paid = $ 1627.36
(‘2) In the given question non constant growth period is not given hence the following assumption has been made
D = 2.36 ( assumed as last paid dividend)
Non constant growth rate = 20 % (Assumed for next year only)
D1 = 2.36 x 1.2
D1 = 2.83
D2 = D1 x 1.055
D2 = 2.99
P1 = D2/(Ke – G)
Where Ke = 12 % (Required rate of return)
G = 5.5 % (Constant growth rate)
P1 = 2.99/(0.12-0.055)
P1 = 45.97
P0 =( D1 + P1 ) / 1.12
P0 = (2.83+45.97)/1.12
P0 = $406.65
Maximum price = $406.65
(‘3) Formula of compounding
FV = PV x (1+ rate/n)Period x n
Where PV = 25000
Rate = 11 %
Period = 30
n=1 ( in annual compounding)
‘n = 365 ( in daily compounding)
Annual Compunding
FV = 25,000 x(1.12)30
FV = 572,307.41
Daily Compounding
FV = 25000 x (1+0.11/365)365 x30
FV = 677,479.07
Difference = 677479.07-572307.41
Difference = $105,171.66
(‘4)
Formula for monthly payment in a mortgage loan
PMT = PV [ i x (1+i)n ]/(1+i)n -1
PMT = 362,000 x [0.05 x (1.05)30]/ (1.05)30 -1
PMT = 362,000 x 0.0651
PMT = $23,548.62
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