__BANK FINANCIAL MANAGEMENT NUMERICALS : 2__

ABM/BFM NUMERICALS

ABM/BFM NUMERICALS

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%?

Explanation :

PV = FV ÷ (1+r)T

= 60000 ÷ 1.3331

= Rs. 45078

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?

Explanation :

NPV = Σ {C÷ (1+r)T} – 1 Total Present Value

= Σ {C÷ (1+r)T}

= (700 ÷ 1.1) + (1000 ÷ 1.21) + (1200 ÷ 1.331)

= Rs. 2364

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?

Explanation :

PV = 20441

NPV = PV – 18000

= Rs. 2441

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

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