0BAFI Business Finance
Semester 3 2010
Explain in simple terms what you would need to know and how you would go about determining the interest and principal components of a loan repayment.
To determine the interest and principal components of a loan repayment you would need to know the following:
Present value (PV) – the amount outstanding on the loan,
r – the discount or interest rate applicable to the loan,
n – the number of payments to be made on the loan,
PMT – the periodic payment (annuity) to be made on the loan.
Using the PV of an annuity formula: you would find the amount of the loan outstanding at a point in time, i.e. the loans PV. From ...view middle of the document...
Beginning with D0, the last dividend paid, we must calculate dividends up to the first year in which the growth rate in dividends becomes constant in perpetuity, which in this case is Year 5:
D0 = $0.50,
D1 = $0.50 (1+0.00) = $0.50,
D2 = $0.50 (1+0.00 ) = $0.50,
D3 = $0.50 (1+0.05) = $0.525,
D4 = $0.525 (1+0.05) = $0.5513,
D5 = $0.5513 (1+0.10) = $0.6064.
Next, we must use the constant growth in dividends pricing formula, , to find the PV of the constantly growing dividends in perpetuity at the end of the period before the constant growth in perpetuity commences. In this example that is at the end of Year 4:
Next, we must find the PV of all the future dividends and P4 by treating them each as single sums and discounting them back to time period 0 (T0) by multiplying them each by the present value interest factor of a single sum, i.e. (1+r)-n :
(note – we do not include the most recent dividend paid, i.e. D0, in the calculation of PV)
P0 = $0.50(1+0.12)-1 + $0.50(1+0.12)-2 + $0.525(1+0.12)-3 + $0.5513(1+0.12)-4 + $30.32(1+0.12)-4
You have just purchased 10 newly issued $100 five year ABC Company Ltd debentures at par. These debentures pay $6 (per debenture) in interest semi-annually. You are also negotiating the purchase of 10 $100 debentures issued by the DEF Company Ltd 4 years ago that return $3 per debenture in semi-annual interest payments and have six years remaining to maturity.
What is the maximum price you should offer for the DEF Company Ltd debentures, assuming the DEF Company Ltd is in the same risk class as the ABC Company Ltd?
Face value = $100,
Coupon PMT = $3,
n = 6 years x 2 coupon payments per year = 12,
r = 6% per half-year (same as coupon rate/yield on ABC Company Ltd debentures as they are in the same risk class).
Use bondprice formula to find the current price of the DEF Company Ltd debentures:
At t = 0 the one-period rate of interest is 6%, the two year rate is 8% per annum, and the three-year rate is 10% per annum. What is the expected two-period interest rate at t = 1?
0 1 2 3
(1+r)3 = (1+r)2 (1+r)1
(1+0.10)3 = (1+r)2 (1+0.06)1
1.331 = (1+r)2 1.06
1.331/1.06 = (1+r)2
1.2557 = (1+r)2
(1.2557)1 = (1+r)2
(1.2557)1/2 = (1+r)2/23
1.1206 = 1+r
1.1206 – 1 = 1-1+r
0.1206 = r
r = 12.06%
Why does it not matter to the price of a share if the intended buyer holds it indefinitely or intends to sell it in some future period?
That a buyer of a share intends selling it in some future period is irrelevant in pricing a share because with the dividend earnings model the current price...