Mountain Energy Company is well known company is energy sector. It produces various equipment used by Hydropower Company. Mountain Energy has issued bonds and common stocks to raise capital. You are…

a. Valuation of Bonds (Present Value)

Mountain Energy’s bonds were issued 10 years ago with the following features:

• Par value (Face value): Rs. 1,000
• Coupon rate: 8.5% (annual, paid yearly)
• Total maturity: 15 years (so 10 years remaining as of today, since they were sold 5 years ago)
• Investor’s required rate of return (YTM): 10%

Step 1: Calculate Annual Coupon Payment

$$\text{Coupon Payment}=\text{Par Value}\times \text{Coupon Rate}=1000\times 0.085=\text{Rs. 85 per year}$$

Step 2: Determine Number of Periods Remaining

Since the bond was issued 10 years ago and has a total maturity of 15 years, 10 years remain until maturity.

Step 3: Apply Bond Valuation Formula

The bond’s value today is the present value (PV) of all future cash flows (coupons + principal) discounted at the required return (10%).

The formula for bond valuation is: $$P=\sum _{t=1}^n\frac{C}{(1+r{)}^t}+\frac{F}{(1+r{)}^n}$$ Where:

• $P$ = Bond price today
• $C$ = Annual coupon payment (Rs. 85)
• $F$ = Face value (Rs. 1,000)
• $r$ = Required return (10% or 0.10)
• $n$ = Years remaining (10)

Step 4: Calculate PV of Coupons (Annuity)

The PV of the coupons is an ordinary annuity: $$P{V}_{\text{coupons}}=C\times \left[\frac{1-(1+r{)}^{-n}}{r}\right]=85\times \left[\frac{1-(1.10{)}^{-10}}{0.10}\right]$$ $$=85\times \left[\frac{1-0.3855}{0.10}\right]=85\times 6.1446=\text{Rs. 522.29}$$

Step 5: Calculate PV of Face Value (Lump Sum)

$$P{V}_{\text{face value}}=\frac{F}{(1+r{)}^n}=\frac{1000}{(1.10{)}^{10}}=\frac{1000}{2.5937}=\text{Rs. 385.54}$$

Step 6: Sum Up to Find Bond Value

$$\text{Bond Value}=P{V}_{\text{coupons}}+P{V}_{\text{face value}}=522.29+385.54=\text{Rs. 907.83}$$

Final Answer: The present value of the bond is Rs. 907.83.

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b. Relationship Between Required Rate of Return and Bond Value

The relationship between the required rate of return (YTM) and the bond’s market value is inverse. This means:

Key Observations:

1. If YTM > Coupon Rate: Bond sells at a discount (as in part a, where YTM = 10% > coupon rate = 8.5%).
2. If YTM < Coupon Rate: Bond sells at a premium.
3. If YTM = Coupon Rate: Bond sells at par value.
4. Interest Rate Risk: Bonds with longer maturities are more sensitive to changes in YTM (higher duration = higher price volatility).

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c. Valuation of Common Stock (Dividend Growth Model)

Mountain Energy’s common stock has the following features:

• Par value: Rs. 100 (irrelevant for valuation)
• Current dividend (D₀): Rs. 20 per share
• Dividend growth rates:
  • First 3 years: 10% per year
  • After 3 years: 5% per year (constant growth)
• Required return (k): 15%

We use the multi-stage dividend growth model because growth is not constant initially.

Step 1: Calculate Dividends for First 3 Years

$$\begin{array}{rl}{D}_1& =D_0\times (1+g_1)=20\times 1.10=\text{Rs. 22}\\ D_2& =D_1\times (1+g_1)=22\times 1.10=\text{Rs. 24.20}\\ D_3& =D_2\times (1+g_1)=24.20\times 1.10=\text{Rs. 26.62}\end{array}$$

Step 2: Calculate Terminal Value (Horizon Value) at Year 3

After year 3, dividends grow at a constant rate ($g_2=5\%$). The terminal value ($P_3$) is calculated using the Gordon Growth Model: $$P_3=\frac{D_4}{k-g_2}=\frac{26.62\times 1.05}{0.15-0.05}=\frac{27.951}{0.10}=\text{Rs. 279.51}$$

Step 3: Discount All Cash Flows to Present (Year 0)

We discount:

1. Dividends for years 1, 2, and 3.
2. Terminal value at year 3.

$$\begin{array}{rl}PV(D_1)& =\frac{22}{(1.15{)}^1}=\frac{22}{1.15}=\text{Rs. 19.13}\\ PV(D_2)& =\frac{24.20}{(1.15{)}^2}=\frac{24.20}{1.3225}=\text{Rs. 18.30}\\ PV(D_3)& =\frac{26.62}{(1.15{)}^3}=\frac{26.62}{1.5209}=\text{Rs. 17.49}\\ PV(P_3)& =\frac{279.51}{(1.15{)}^3}=\frac{279.51}{1.5209}=\text{Rs. 183.76}\end{array}$$

Step 4: Sum Up Present Values

$$\text{Stock Value}=PV(D_1)+PV(D_2)+PV(D_3)+PV(P_3)=19.13+18.30+17.49+183.76=\text{Rs. 238.68}$$

Final Answer: The present value of the stock is Rs. 238.68.

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