Question

A bond having a face value (F) of Rs.100 is selling at (B) Rs.95 in the market. It pays coupon semi-annually and coupon rate is 10% per annum. It has just paid the last coupon on yesterday and there are 2 more coupon payments left. The first one will be paid exactly 6 months from now and last one exactly 1 year from now. The Face Value will be repaid at maturity along with last coupon payment.
Draw the cash flow diagram demarking the inflows and outflows with timings.	(1)
What is the Current Yield of the bond?	(1)
What is the Yield to Maturity of the bond?	(3)
What will be the new bond price if the yield decreases by 50 basis points?	(2)

Answer 1

Face Value of the bond = Rs 100 | Current Price of the bond = Rs 95

Coupon rate = 10% semiannual

Coupon payment = Face Value * Coupon rate / 2 = 100 * 10% / 2 = Rs 5

As per the given future coupon payment details of one at 6 months and second at 1 year along-with Face value, below is the Cashflow Diagram drawn on Excel with periods marked for each cashflow:

Current Yield of a bond = Annual Coupon Payment / Current Price of the bond

Annual Coupon Payment = 10% * 100 = Rs 10 | Current Price = Rs 95

Current Yield of the Bond = 10 / 95 = 10.53%

Now we will calculate the YTM of the bond, using the formula for Price of a bond, which is the sum of Present Value of all the cash-inflows.

Price of the bond = Coupon Payment at 6 months / (1 + YTM / 2) + (Coupon at 1 year + Face Value) / (1+YTM/2)²

We are taking YTM / 2 because of semiannual payments of coupon.

We already know the price of the bond, which is Rs 95. The cashflows are also known. We will solve the above expression for YTM.

=> 95 = 5 / (1+YTM/2) + 105 / (1+YTM/2)²

Let (1 / (1+YTM/2)) be X

=> 105X² + 5X - 95 = 0

Using Quadratic formula, X = (-b (b² - 4ac)^1/2) / 2a | We can solve for the roots.

Roots: X = -0.97530 and 0.92768

As YTM will be positive value, hence, using the Positive root X = 0.92768 for calculation of YTM

Since (1 / (1+YTM/2)) = X, we can use the calculated value for X and Find YTM

=> (1 / (1+YTM/2)) = 0.92768

=> 1 = 0.92768 + 0.46384YTM

=> YTM = (1 - 0.92768) / 0.46384

YTM of the Bond = 0.1559 or 15.59%

As YTM decreases by 50 basis points, which is 0.50%, New YTM = 15.59% - 0.50% = 15.09%

Using the New YTM, we can calculate the Price of the Bond.

Price of the bond = Coupon Payment at 6 months / (1 + YTM / 2) + (Coupon at 1 year + Face Value) / (1+YTM/2)²

Price of the bond = 5 / (1 + 15.09% / 2) + 105 / (1 + 15.09%/2)²

Price of the bond = 4.65 + 90.78

Price of the bond if the YTM increases by 50 basis points = Rs 95.43