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Government Bonds Valuation and Investment

XAT 2010 · Quantitative Ability & Data Interpretation · Hard · Quantitative Ability

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Passage / data set

Answer the questions based on the information given below:

Madhubala Devi, who works as a domestic help, received Rs. 2500 as Deepawali bonus from her employer. With that money she is contemplating purchase of one or more among 5 available government bonds - A, B, C, D and E.

To purchase a bond Madhubala Devi will have to pay the price of the bond. If she owns a bond she receives a stipulated amount of money every year (which is termed as the coupon payment) till the maturity of the bond. At the maturity of the bond she also receives the face value of the bond.

Price of a bond is given by: P=[∑t=1TC(1+r)t]+F(1+r)TP = [\sum_{t=1}^{T} \frac{C}{(1+r)^t}] + \frac{F}{(1+r)^T}

where C is coupon payment on the bond, which is the amount of money the holder of the bond receives annually; F is the face value of the bond; T is the number of years in which the bond matures; R=0.25R = 0.25, which means the market rate of interest is 25%.

Among the 5 bonds the bond A and another two bonds mature in 2 years, one of the bonds matures in 3 years, and the bond D matures in 5 years.

The coupon payments on bonds A, E, B, D and C are in arithmetic progression, such that the coupon payment on bond A is twice the common difference, and the coupon payment on bond B is half the price of bond A.

The face value of bond B is twice the face value of bond E, but the price of bond B is 75% more than the price of bond E. The price of bond C is more than Rs. 1800 and its face value is same as the price of bond A. The face value of bond A is Rs. 1000.

Bond D has the largest face value among the five bonds.

Question 1 of 3

The face value of bond E must be

  1. A.

    Rs. 1406.25

  2. B.

    Rs. 1686.25

  3. C.

    Rs. 2250.50

  4. D.

    Rs. 2812.50

  5. E.

    Rs. 3372.50

Answer

A

Explanation

Solving the bond equations step by step: Coupon A = 2d, E = 3d, B = 4d, D = 5d, C = 6d. Price A = 8d=1000  ⟹  d=1258d = 1000 \implies d = 125. Coupons: A=250, E=375, B=500, D=625, C=750. Face value C = Price A = 1000. Price C > 1800 with T=3   ⟹  \implies Price C = 1976. Solving system for B and E (maturing in 2 years) gives Price E = 1440, Face Value E = 1406.25.

Question 2 of 3

Madhubala Devi purchased one or more of the 5 available bonds from her bonus pay and spent the remainder. She made the purchase decision such that her return from the bonds is maximized. Her return from the bonds is

  1. A.

    Rs. 3000.00

  2. B.

    Rs. 3250.00

  3. C.

    Rs. 3656.25

  4. D.

    Rs. 3906.25

  5. E.

    Rs. 4531.25

Answer

C

Explanation

With Rs 2500, options are:

  1. Buy Bond A (1000) + Bond E (1440) = 2440 cost. Return = Face Values + Total Coupons = 1000+2(250)+1406.25+2(375)=3656.251000 + 2(250) + 1406.25 + 2(375) = 3656.25.
  2. Buy Bond C (1976). Return = 1000+3(750)=32501000 + 3(750) = 3250. Maximum return = Rs 3656.25.

Question 3 of 3

The price of bond C must be

  1. A.

    Rs. 1825

  2. B.

    Rs. 1874

  3. C.

    Rs. 1925

  4. D.

    Rs. 1976

  5. E.

    Rs. 2342

Answer

D

Explanation

Price of C for T = 3 years: PC=7501.25+7501.252+7501.253+10001.253=600+480+384+512=1976.P_C = \frac{750}{1.25} + \frac{750}{1.25^2} + \frac{750}{1.25^3} + \frac{1000}{1.25^3} = 600 + 480 + 384 + 512 = 1976.

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