An investor is considering purchasing a 5 year bond of ₹1,00,000 at par value and an annual fixed coupon rate of 12% while coupon payments are made semi-annually. The minimum yield that the investor would accept is 6.75%. Find the fair value of the bond.

Question

Accepted Answer

> [!TLDR]
> The fair value is the present value of the semi-annual coupons plus the par value, discounted at the investor's required semi-annual yield. Because the 12% coupon far exceeds the 6.75% yield, the bond trades at a premium: its fair value is about **₹1,21,977** (well above par).

Coupons are semi-annual: coupon $=\dfrac{12\%}{2}	imes1{,}00{,}000=₹6{,}000$ every six months for $n=10$ periods; the required semi-annual yield is $r=\dfrac{6.75\%}{2}=3.375\%=0.03375$; par ₹1,00,000 is repaid at maturity.

1. **Discount factor.** $(1.03375)^{-10}=0.717437$.
2. **PV of the coupons.**
$$6{,}000	imes\frac{1-0.717437}{0.03375}=6{,}000	imes8.37224=₹50{,}233.$$
3. **PV of the par value.**
$$1{,}00{,}000	imes0.717437=₹71{,}744.$$
4. **Fair value.** $50{,}233+71{,}744=₹1{,}21{,}977$. …

Q.An investor is considering purchasing a 5 year bond of ₹1,00,000 at par value and an annual fixed coupon rate of 12% while coupon payments are made semi-annually. The minimum yield that the investor would accept is 6.75%. Find the fair value of the bond.

Concept understanding — Bond Valuation

Bond Valuation: The Intuition First

The Precise Statement

Why This Works: The Logic

A Worked Example

Step 1 — set up the valuation

Step 2 — compute the discount factors (14%)

Step 3 — combine and solve

Step 1 — Identify the cash flows

Step 2 — Discount each cash flow

Step 3 — Add them up

Q.An investor is considering purchasing a 5 year bond of ₹1,00,000 at par value and an annual fixed coupon rate of 12% while coupon payments are made semi-annually. The minimum yield that the investor would accept is 6.75%. Find the fair value of the bond.

🎓Unlock everything free for 14 days

Unlock everything free for 14 days