10 years ago, the City of Melrose issued $3,000,000 of 8% coupon, 30-year, semiannual payment, tax-exempt muni bonds. 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 6% of the face amount. New 20-year, 6%, semiannual payment bonds can be sold at par, but flotation costs on this issue would be 2% 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.

the net present value of the refunding = $453,443

Explanation:

Given that:

Amount issued by  City of  Melrose = $3,000,000

Old rate of coupon = 8%

Period (years) = 20

Call premium = 6%

New rate coupon = 6%

Flotation cost = 2%

For the cost of refunding ; we have:

Call premium = 6% × $3,000,000

Call premium = 0.06  × $3,000,000

Call premium = $180000

Floatation cost = 2%  × $3,000,000

Floatation cost = 0.02 × $3,000,000

Floatation cost = $60000

The total investment outlay = Call premium + Flotation cost

The total investment outlay = $180000  + $60000

The total investment outlay = $240000

However, the interest on the old bond per  6 months = (old coupon/2 )  × Amount issued

the interest on the old bond per  6 months = (8%/2)  ×  $3000000

the interest on the old bond per  6 months = (0.08/2) ×  $3000000

the interest on the old bond per  6 months = 0.04 ×  $3000000

the interest on the old bond per  6 months = $120000

the interest on the new bond per  6 months = (new coupon/2 )  × Amount issued

the interest on the new bond per  6 months = (6%/2)  ×  $3000000

the interest on the new bond per  6 months = (0.06/2) ×  $3000000

the interest on the new bond per  6 months = 0.03  ×  $3000000

the interest on the new bond per  6 months = $90000

Amount savings per 6 months = $120000 - $90000

Amount savings per 6 months = $30000

Finally, the present value for the savings = 30000 × PVIFA(0.03,40)

the present value for the savings = $693,443

Thus;

the net present value of the refunding = the present value for the savings - Cost of refunding

the net present value of the refunding = $693,443 - $240000

the net present value of the refunding = $453,443

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