CAIIB-ABM/ BFM- NUMERICALS/CASE STUDIES 1. Kumar invested in 10%, 3-year bond of face value of Rs. 1000. The expected market rate is 12%. What is the duration of the bond?
Explanation : Bond’s Duration = ΣPV×t ÷ ΣP Bond Price = (1/(1+R)^t)((coupon*((1+R)^t-1)/R)+Face Value) ΣP = {100 × (1.123 -1) ÷ 0.12 + 1000} ÷ 1.123 = 951.6 Here 1 ÷ 1.12 = 0.89286, so a^t = 0.711787 ΣPV × t = 100 × 8.33336 × [0.288213 ÷ 0.10714286 – 3 × 0.711787] + 3000 × 0.711787 = 833.336 × (2.689988 – 2.135361) + 2135.361 = 462.19 + 2135.36 = 2597.55 So, Duration of the Bond = 2597.55 ÷ 951.6 = 2.73 years
2. Gaurav invested in 12.5%, 5-year bond of face value of Rs. 100. The expected market rate is 15%. What is the duration of the bond?
Explanation : Bond’s Duration = ΣPV×T ÷ ΣP Bond Price = (1/(1+R)^t)((coupon*((1+R)^t-1)/R)+Face Value) ΣP = {12.5 × (1.155 -1) ÷ 0.15 + 100} ÷ 1.155 = 91.6196 Here a = 0.86956 and a^t = 0.497176 So, ΣPV × T = 12.5 × 6.66636 × {0.502824 ÷ 0.13044 – 2.4588} + 248.588 = 116.33046 + 248.588 = 364.92 So, Duration of the Bond = 364.92 / 91.6196 = 3.98 years
3. Albert purchased 8%, 3 years bond of Rs. 10 lac, with annual interest payment and face value payable on maturity. The YTM is assumed@ 6%. Calculate the duration and modified duration.
Explanation : Bond’s Duration = ΣPV×T ÷ ΣP ΣP = 1053421 Now, a = 0.943396 and a^t = 0.839619 So, ΣPV×T = 80000 × 16.666 × (0.160381÷0.056604 – 2.518857) + 2518857 = 419370.767 + 25188579 = 2938227.77 So, Duration of the Bond = 2938227.77 / 1053421 = 2.79 years & Modified Duration = Mckauley Duration ÷ (1 + R) = 2.79 ÷ 1.06 = 2.63
4. Salim purchased 8%, 3 years bond of Rs. 10 lac, with annual interest payment and face value payable on maturity. The YTM is assumed@ 6%. Calculate % change in the price of the bond when the decrease in YTM is 100 basis points from 6% to 5% and the duration is 2.79 years and modified duration is 2.63 years.
Explanation : Percentage change in price of bond = -MD × Change in Price = -2.63 × (6% - 5%) = 2.63%, That means a fall in YTM by 1% increases the price of the bond by 2.63%.
5. A 12%, 4-year bond of Rs. 100 was purchased by x for Rs. 100. If the market interest rate increased by 1%, what will the market price?
Explanation : P = 100 CR = 12% YTM = 12 + 1 = 13% So, Price = 97.03
6. Mitalee is to receive Rs. 60000 from bank at the end of 3 years, being the maturity value of a term deposit. How much he is depositing now, if the interest rate is 10%?
7. The cash flow expected from a project is Rs. 700, Rs. 1000 and Rs. 1200 in the 1st, 2nd, & 3rd year. The discounting factor @ 10% roi is 1.10, 1.21 and 1.331. What is the total present value of these cash flows?
8. Priyanka made an investment of Rs. 18000 and he expects a return of Rs. 3000 p.a. For 12 years. What is the present value and net present value of the cash flow @ 10% discount rate?
9. Current yield on an 8% Rs. 100 bond is 7.5%. The price of the bond is ......
Explanation : Bond Price = (1/(1+R)^t)((coupon*((1+R)^t-1)/R)+Face Value) (Here, t = 1 So, price = (Coupon + Face Value) ÷ (1 + R) = (8 + 100) ÷ 1.075 = 100.465) But, since Coupon Interest = Current Yield × Current Market Price So, Price = 8 ÷ 7.5% = 8000 ÷ 75 = 106.67
10. A 6 year bond is selling at Rs. 9500 with face value of Rs. 10000. The annual Coupon amount is 800. What is the yield to maturity?
Explanation : Since Coupon rate = 8% and market price < Face Value, so YTM must be > CR Let CR be 9%. So, bond’s price = 9551.41 > 9500 Let CR be 10%, so price = 9128.95 < 9500 So, YTM must lie between 9 & 10. Using interpolation technique, YTM = 9% + (10-9) % × (9551.41 – 9500) ÷ (9551.41 – 9128.95) = 9+51.41/422.46 = 9.12%
11. A 15 year bond is trading at Rs. 958 with face value of Rs. 1000. The Coupon rate is 8%. What is the yield to maturity?
Explanation : Since trading value < face value, YTM is > CR At 7%, price = 1091.08 > 958 And at YTM = 9%, price = 919.39 < 958, so YTM lies somewhere between 7 and 9. = 7 + (9-7) × (1091.08 – 958) / (1091.08 – 919.39) = 7 + 2 × 133.08 / 171.69 = 8.5%
12. A 3 year bond with par value Rs. 1000 has Coupon rate 12%. If the required rate of return is 10% and interest is payable semi - annually, find the value of the bond.
Explanation : Here, interest is calculated semi-annually, so Coupon = 1000 × 12% ÷ 2 = 60, YTM = 10%/2 = 0.05, T = 3 × 2 = 6 years So, price = 1050
13. The yield on a 6-year bond is 12% while that of 4-year bond is 9%. What should be the yield on a 2-year bond beginning from now? Explanation : (1+12%)^6 = (1+9%)^4 × (1+r)^2 R = 18%
14. A bond is issued with a face value of 1000 that pays a Rs. 25 Coupon semi-annually. Find its Coupon rate.
Explanation : Coupon = Face Value × Coupon Rate 25 = 1000 × CR ÷ 2 So, CR = 5%
15. A 2-year bond offers a yield of 6% and a 3-year bond offers a yield of 7.5%. Under the expectation theory, what should be the yield on a 1-year bond in 2 years?
Explanation : (1+7.5%)^3 = (1+6%)^2 × (1+r)^1 R = 10.56%
16. Find the price of a zero-Coupon bond maturing in 5 years and has a par value of 1000 and a required yield of 6%.
Explanation : Using bond’s price formula, here Coupon = 0 and hence, Zero-Coupon Bond’s price = Face Value ÷ (1 + R)T = 1000 ÷ 1.065 But, unless otherwise mentioned, the required yield of most zero-Coupon bonds is based on a semi-annual Coupon payment. So, Price = 1000 ÷ 1.0310 = 744
17. A bond with a par-value of Rs. 100 is purchased for 95.92 and it paid a Coupon rate of 5%. Calculate its current yield. Explanation : Coupon = Face value × Coupon Rate And annual interest paid = Market Price × Current Yield 5 = 95.92 × CY CY = 0.0521 = 5.21%
18. A zero-Coupon bond has a future value of Rs. 1000 and matures in 2 years and can be currently purchased for Rs. 925. Calculate its current yield.
Explanation : Here 1000 = 925 × (1 + r)^2 So, r = 1.0398 – 1 = 0.0398 = 3.98%
19. You are receiving Rs. 1000 every year for the next 5 years at the beginning of the period and you invest each payment @ 5%. How much you would at the end of the 5-year period?
Explanation : Apply FV formula to get the Answer = 5802
20. An annuity consists of monthly repayments of Rs. 600 made over 20 years and if rate is 14% monthly. What is the future value of the annuity? Explanation : Apply FV formula to get the Answer Here R = 14% / 12 = 0.01166 T = 20 × 12 = 240 FV = 781146