Please show work, no excel. Your firm has an obligation to pay a parts supplier
ID: 2811821 • Letter: P
Question
Please show work, no excel.
Your firm has an obligation to pay a parts supplier eight equal annual payments of $14,000,000 (the first payment is due 1 year from today). Assume the Treasury yield curve is a flat 4.25%, and today your firm purchases zero-coupon Treasury bonds to fund and immunize the obligation. All bonds that your firm purchases have the same maturity.
a. (4 points) Calculate the present value and duration of the obligation (carry the duration out to four decimal places).
b. (6 points) What is the total face value of the bonds your firm buys (In your calculations, make sure you use all 4 decimal places in the duration you calculated in part a)
c. (10 points) If immediately after purchasing the bonds the yield curve increases to a flat 4.63%, by how much (in dollars) will the obligation be underfunded or overfunded? Be sure to list the dollar amount and to write whether the obligation is underfunded or overfunded.
Explanation / Answer
a. Assuming the discount rate of 4.25% which is the flat Treasury yield curve, step-by-step-calculation of the present value (PV) of the cash flows of the obligation is as shown below:-
$ 399
Therefore, the PV of the obligations is United States Dollar (USD) 399 million.
Assuming the firm purchases zero-coupon coupon at a flat treasury yield curve of 4.25%, the par value of the coupon needs to be calculated where 4.25% of the Bond's par value is equal to USD 14 million annually.
Par value of the zero-coupon bond (G) = 14/4.25% i.e. USD 329 million
Macaulay duration of the obligation, (H) = (F)/(G) = 1.2127 years
(b) Total face value of the debt teh firm buys is USD 329 million as calcualted in part (a)
(c) Bond cash flows' valuation at a treasury yield of 4.25% is shown below:-
Bond cash flows' valuation at a treasury yield of 4.63% will have an annual interest rate of USD 15 million i.e. 4.63% of Bond'a par value of USD 329 million
A bond's price is inversely proportional to the bond yield. Therefore with an increase of the treasury zero-coupon bond's yield from 4.25% to 4.63% per annum, the bond's price will reduce from USD2,288 million (See F1 above) to USD2,261 million (See F2 above). Therefore, the frim's obligations will be underfunded by an amount of USD 27 million i.e. difference between F1 and F2
All figures below are in USD million unless mentioned otherwise Year No. (A) Scheduled Debt Obligations' Cash Flows (B) Year Weighted Value of Debt Obligations' Cashflows(C) = (A)*(B) Discount factor based on treasury yield curve of 4.25% (D) = 1/{(1+4.25%)}^(A) Present Value of Weighted Value of Debt Obligations' Cashflows (E)=(C)*(D) 1 $ 14 $ 14 0.96 $ 13 2 $ 14 $ 28 0.92 $ 26 3 $ 14 $ 42 0.88 $ 37 4 $ 14 $ 56 0.85 $ 47 5 $ 14 $ 70 0.81 $ 57 6 $ 14 $ 84 0.78 $ 65 7 $ 14 $ 98 0.75 $ 73 8 $ 14 $ 112 0.72 $ 80 Total (F)
$ 399