Check Your Work heducation.com/hm.tpx You will be paying $12,800 a year in tuiti
ID: 2791906 • Letter: C
Question
Check Your Work heducation.com/hm.tpx You will be paying $12,800 a year in tuition expenses at the end of the next two years. Bonds currently yield 8%. a. What is the present value and duration of your obligation? (Do not round Intermediate calculations. Round "Present value" to 2 decimal places and "Duration" to 4 decimal places.) Present value Duration years b. What is the duration of a zero-coupon bond that would immunize your obligation and its future redemption value? (Do not round Intermediate calculations. Round "Duration" to 4 decimal places and "Future redemption value" to 2 decimal places.) Duration Future redemption value You buy a zero-coupon bond with value and duration equal to your obligation. c-1. Now suppose that rates immediately increase to 9%, what happens to your net position, that is, to the difference between the value of the bond and that of your tuition obligation? (Enter your answer as a positive value. Do not round intermediate calculations. Round your answer to 2 decimal places.) Net position changes by s c-2. What if rates fall to 7%? (Enter your answer as a positive value. Do not round intermediate calculations. Round your answer to 2 decimal places.) Net position changes by 27Explanation / Answer
1) To calculate the present value, we will multiply tuition expense with the present value factor. Please refer to present value table for PV factors.
Year
Tuition Expense
Present Value Factor @ 8%
Present Value
Weight of Cash flow
Time-period x Weight
1
$12,800.00
0.925926
$11,851.85
0.519231
0.519231
2
$12,800.00
0.857339
$10,973.94
0.480769
0.961538
Present Value all payments going towards tuition expense = $11,851.85 + $10,973.94 = $22,825.79
Weight of cash flow = PV of cash flow in the year / Total PV
Duration = (Time period x Weight of cash flow)
=> 0.519231 + 0.961538 = 1.480769
b) In order to immunize your obligation to pay $12,800 at the end of next two years, the duration of zero-coupon bond must be equal to the duration calculated in part a i.e. duration of tuition expense, which is 1.480769
Future value of zero-coupon bond would be equal to its face value, which is calculated below:
Face Value of zero coupon bond = Present value x (1+interest rate)years to maturity
=> $22,825.79 x (1+0.08)1.480769
= $25,581.07
So, the future redemption value of zero-coupon bond will be $25,581.07
c-1) The net position would be equal to the difference of present value of tuition expenses and present value of zero-coupon bond. So, we first need to calculate the present value of both things with changed interest rate of 9%.
Present value of zero-coupon bond = $25,581.07 / (1.09)1.480769
=> $25,581.07 / 1.136108994 = $22,516.39
Present value of tuition expense = ($12,800 / 1.091) + ($12,800 / 1.092)
=> $11,743.12 + $10,773.50 = $22,516.62
Change in Net position = $22,516.62 - $22,516.39 = $0.24
So, the net position would increase by $0.24
c-2) Present value of zero-coupon bond = $25,581.07 / (1.07)1.480769
=> $25,581.07 / 1.105377416 = $23,142.38
Present value of tuition expense = ($12,800 / 1.071) + ($12,800 / 1.072)
=> $11,962.62 + $11,180.02 = $23,142.63
Change in Net position = $23,142.63 - $23,142.38 = $0.25
So, the net position would increase by $0.25
Year
Tuition Expense
Present Value Factor @ 8%
Present Value
Weight of Cash flow
Time-period x Weight
1
$12,800.00
0.925926
$11,851.85
0.519231
0.519231
2
$12,800.00
0.857339
$10,973.94
0.480769
0.961538