# The City of Charleston issued $3,000,000 of 8% coupon, 30 year, semiannual payment, tax-exempt... ## Question: The City of Charleston issued$3,000,000 of 8% coupon, 30 year, semiannual payment, tax-exempt muni bonds 10 years ago. The bonds had 10 years of call protection, but now the bonds can be called if the city chooses to do so. The call premium would be 7.50% of the face amount. New 20 year, 6%, semiannual payment, bonds can be sold at par, but flotation costs on this issue would be 3.0% of the amount of bonds sold.

What is the net present value of the refunding? Note that cities pay no income taxes, hence taxes are not relevant.

## Interest

Interest is the amount which borrowers pay to the investor for using a particular amount of money or any other asset. It is reported to the profit and loss account. Interest can be charged annually, semi-annually quarterly or monthly.

{eq}\begin{align*} \rm\text{Call premium} &= \rm\text{Issued bond amount} \times \rm\text {Interest rate}\\ &= \$3,000,000 \times \dfrac{6}{100}\\ &= \$ 180,000 \end{align*} {/eq}

Calculating the flotation cost

{eq}\begin{align*} \rm\text{Flotation cost} &= \rm\text{Issued bond amount} \times \rm\text {Interest rate}\\ &= \$3,000,000 \times \dfrac{3}{100}\\ &= \$ 180,000 \end{align*} {/eq}

Calculating the total investment outlay:

 Particular Amount Call premium $180,000 Flotation cost$60,000 Total investment outlay 240,000 Calculating the interest on old bond {eq}\begin{align*} \rm\text{Interest on old bond} &= \rm\text{Issued bond amount} \times \rm\text {Interest rate} \times \dfrac{\rm\text{Number of month}} {{12}}\\ &= \ 3,000,000 \times \dfrac{8}{100} \times \dfrac{6}{12}\\ &= \120,000 \end{align*} {/eq} Calculating the interest on new bond {eq}\begin{align*} \rm\text{Interest on new bond }&= \rm\text{Issued bond amount } \times \rm\text{ Interest rate} \times \dfrac{\rm\text{Number of month}}{{12}}\\ &= \ 3,000,000 \times \dfrac{6}{100}\times \dfrac{6}{12}\\ &= \90,000 \end{align*} {/eq} Calculating the saving per six month bond  Particular Amount Interest on old bond120,000 Interest on new bond $90,000 Saving per six month$30,000

P.V.F for 40 period @3% is 23.114

{eq}\begin{align*} \rm\text{Present value of saving} &= \rm\text{Saving} \times \rm\text{ Present value factor}\\ &= \$30,000\times 23.114\\ &= \$ 693,443 \end{align*} {/eq}

Calculating the NPV of refunding

{eq}\begin{align*} \rm\text{NPV of refunding} &= \rm\text{ Present value of saving} - \rm\text{ Total investment outlay}\\ &= \$693,443 - \$ 240,000\\ &= \\$ 453,443 \end{align*} {/eq} 