Investment X offers to pay you Rs. 40,000 per year for 9 years, whereas investment Y offers to pay you Rs. 60,000 for 5 years. If the discount rate is 5%, which of these cash flow stream has the highest present value?
- A company issues Rs. 2,50,000, 12% debentures to be redeemed after the expiry of 8 years. Cost of issue is 5% and the tax rate is 50%. Compute the cost of debt. 13. The sales of a firm are 1000 units. Selling price per unit is Rs.10 and the variable cost per unit.
The Correct Answer and Explanation is:
1. Present Value Comparison of Investment X and Y
Investment X:
- Annual payment = Rs. 40,000
- Duration = 9 years
- Discount rate = 5%
Using the Present Value of an Annuity formula: PV=C×[1−(1+r)−nr]PV = C \times \left[\frac{1 – (1 + r)^{-n}}{r}\right] PVX=40,000×[1−(1+0.05)−90.05]=40,000×7.1078=Rs. 2,84,312PV_X = 40,000 \times \left[\frac{1 – (1 + 0.05)^{-9}}{0.05}\right] = 40,000 \times 7.1078 = \text{Rs. 2,84,312}
Investment Y:
- Annual payment = Rs. 60,000
- Duration = 5 years
- Discount rate = 5%
PVY=60,000×[1−(1+0.05)−50.05]=60,000×4.3295=Rs. 2,59,770PV_Y = 60,000 \times \left[\frac{1 – (1 + 0.05)^{-5}}{0.05}\right] = 60,000 \times 4.3295 = \text{Rs. 2,59,770}
✅ Investment X has the higher present value (Rs. 2,84,312).
2. Cost of Debt (Kd) Calculation
Given:
- Face value = Rs. 2,50,000
- Coupon rate = 12% → Interest = Rs. 30,000
- Life = 8 years
- Cost of issue = 5% → Net proceeds = 95% of Rs. 2,50,000 = Rs. 2,37,500
- Tax rate = 50%
Formula for Cost of Debt (Kd): Kd=I(1−T)+(F−NP)nF+NP2Kd = \frac{I(1 – T) + \frac{(F – NP)}{n}}{\frac{F + NP}{2}}
Where:
- II = Interest = 30,000
- TT = Tax rate = 0.5
- FF = Face value = 2,50,000
- NPNP = Net proceeds = 2,37,500
- nn = 8
Kd=30,000(1−0.5)+(2,50,000−2,37,500)82,50,000+2,37,5002=15,000+1,562.52,43,750=16,562.52,43,750=0.0679 or 6.79%Kd = \frac{30,000(1 – 0.5) + \frac{(2,50,000 – 2,37,500)}{8}}{\frac{2,50,000 + 2,37,500}{2}} = \frac{15,000 + 1,562.5}{2,43,750} = \frac{16,562.5}{2,43,750} = 0.0679 \text{ or } 6.79\%
✅ Cost of debt (after tax) = 6.79%
3. Incomplete Sales & Cost Data
The third question appears incomplete:
- Sales = 1000 units
- Selling Price = Rs. 10 per unit
- Variable cost per unit = [Missing]
Assuming variable cost = Rs. 6/unit:
- Revenue = 1000 × 10 = Rs. 10,000
- Variable Cost = 1000 × 6 = Rs. 6,000
- Contribution Margin = 10,000 – 6,000 = Rs. 4,000
If you clarify the missing variable cost, I can provide precise profitability and break-even analysis.
Conclusion
Investment analysis often revolves around comparing future cash inflows using present value techniques. Investment X provides a smaller annual payout (Rs. 40,000), but over a longer period (9 years), while Investment Y offers Rs. 60,000 but only for 5 years. Applying the annuity formula with a 5% discount rate, Investment X results in a present value of Rs. 2,84,312, exceeding Investment Y’s Rs. 2,59,770. This demonstrates the impact of the time value of money — receiving payments over a longer period can outweigh larger but shorter-term inflows.
In corporate finance, the cost of debt is crucial in determining the company’s cost of capital. For debentures of Rs. 2,50,000 issued at a 5% cost with an annual 12% coupon and 50% tax rate, the net proceeds are Rs. 2,37,500. The after-tax cost of debt is calculated as 6.79%, showing how tax shields reduce the effective borrowing cost.
Finally, the third question requires clarification on the variable cost per unit to complete profitability analysis. Assuming a Rs. 6 variable cost, the firm generates a contribution of Rs. 4,000 from sales of 1000 units. This margin helps cover fixed costs and contribute to net profits. Understanding these figures aids in strategic decisions such as pricing, production scaling, or cost control.
