Question 6.S2.2: A company issues a new 15 per cent debentures of Rs 1,000 fa......
A company issues a new 15 per cent debentures of Rs 1,000 face value to be redeemed after 10 years The debenture is expected to be sold at 5 per cent discount. It will also involve floatation costs of 2.5 per cent of face value. The company’s tax rate is 35 per cent. What would the cost of debt be? Illustrate the computations using (i) trial and error approach and (ii) shortcut method.
(i) Trial and Error/Long Approach
Cash flow pattern of the debenture would be as follows:
We are to determine the value of k_{d} in the following equation:
\text { Rs } 925=\sum\limits_{t=1}^{10} \frac{\text { Rs } 97.5}{\left(1 + k_{d}\right)^{t}}+\frac{\text { Rs } 1,000}{\left(1 + k_{d}\right)^{10}}
The value of k_{d} for this equation would be the cost of debt. The value of k_{d} can be obtained, as in the case of IRR, by trial and error.
Determination of \mathbf{PV} at 10 \% and 11 \% rates of interest
(ii) Shortcut Method: The formula for approximating the effective cost of debt can, as a shortcut, be shown in the Equation (6.7):
k_{d}=\frac{I(1 – t) + (f + d + p r – p i) / N_{m}}{(R V + S V) / 2} (6.7)
\begin{aligned}& N_{m}=\text { Term of debt } \\& f=\text { Flotation cost } \\& d=\text { Discount on issue of debentures } \\& p i=\text { Premium on issue of debentures } \\& p r=\text { Premium on redemption of debentures } \\& t=\text { Tax rate } \\& \qquad k_{d}=\frac{R s 150(1-0.35)+(\text { Rs } 50+\text { Rs } 25) / 10}{(\text { Rs } 925+\text { Rs } 1,000) / 2}=10.9 \text { per cent }\end{aligned}
| Years | Cash flow |
| 0 | + Rs 925 (Rs 1,000 – Rs 75, that is, par value less |
| flotation cost less discount) | |
| 1 – 10 | – Rs 150 (interest outgo) |
| 10 | – Rs 1,000 (repayment of principal at maturity). |
| Year(s) | Cash | PV factor at | Total PV at | ||
| outflows | 10% | 11% | 10% | 11% | |
| 1-10 | Rs 97.5 | 6.145 | 5.889 | Rs 599.14 | Rs 574.18 |
| (Table A-4) | |||||
| 10 | 1,000 | 0.386 | 0.352 | 386.00 | 352.00 |
| (Table A-3) | |||||
| 985.14 | 926.18 | ||||
The value of k_{d} would be 11 per cent.