Question

You have estimated spot rates as follows: ri = 5.00%, r2 = 5.40%, r3 = 5.70%, r4 = 5.90%, rs = 6.00%. a. What are the discount factors for each date (that is, the present value of $1 paid in year 6)? (Do not round intermediate calculations. Round your answers to 3 decimal places.) Year Discount Factors b. Calculate the PV of the following $1,000 bonds assuming an annual coupon and maturity of: (i) 5%, two-year bond; (ii) 5%, five-year bond; and (iii) 10%, five-year bond. (Do not round intermediate calculations. Round your answers to 2 decimal places.) Present Value b-i. 5%, two-year bond b-ii. 5%, five-year bond b-iii. 10%, five-year bond

Answer 1

Please refer to below spreadsheet for calculation and answer. Cell reference also provided.

Year Spot rate 5.00% 5.40% 5.70% 5.90% 6.00% Discount Factors 0.952 0.900 0.847 0.795 0.747 5 Cash Flow Year Spot rate 5%, two year bond 5%, five year bond 10%, five year bond 1 1 2 3 4 5 $50.00 $1,050.00 Discount Factors 0.952 0.900 0.847 0.795 0.747) 5.00% 5.40% 5.70% 5.90% 6.00% $50.00 $50.00 $50.00 $50.00 $1,050.00 $100.00 $100.00 $100.00 $100.00 $1,100.00 b-i 5%, two year bond b-ii 5%, five year bond b-iii 10%, five year bond Present value $992.79 $959.34 $1,171.43 20 21 22

Cell reference -

B DE Year Spot rate Discount Factors 0.05 0.054 0.057 0.059 0.06 =1/(1+C3)^B3 =1/(1+C4)^B4 =1/(1+C5^B5 =1/(1+C6)^B6 =1/(1+C7)^B7 Cash Flow Discount Factors 5%, two year bond 5%, five year bond 10%, five year bond Year 10 Spot rate 0.05 12 0.054 13 0.057 14 0.059 15 0.06 16 17 Present value 18 b-i 5%, two year bond =SUMPRODUCT(D11:D12, E11:E12) =SUMPRODUCT(D11:D15,F11:F15) 20 b-iii 10%, five year bond -SUMPRODUCT(D11:015,G11:G15) =1/(1+C11)^B11 55%*1000 =1/(1+C12)^B12 =E11+1000 =1/(1+C13)^B13 =1/(1+C14)^B14 =1/(1+C15)^B15 =5%*1000 =5%* 1000 =5%*1000 =5%* 1000 =5%*1000+1000 =10%*1000 =10%*1000 =10%*1000 = 10%*1000 =10%*1000+1000

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