Question

Orlando advertised for bids for the purchase of $3 million principal amount of Waste Water Revenue Bonds. Bonds will be delivered on April 1, 2021, and the interest will be paid on April 1st of the following years. The bonds mature as follows:
Maturity Date
Amount ($)
4/1/2025
100,000
4/1/2026
100,000
4/1/2027
100,000
4/1/2028
100,000
4/1/2029
200,000
4/1/2030
200,000
4/1/2031
250,000
4/1/2032
250,000
4/1/2033
250,000
4/1/2034
700,000
4/1/2035
750,000
The City received three competing bids for the Waste Water Revenue Bonds. The three offers are as follows:
From Rogue Securities:
• The City receives $3.5 million dollars
• The Interest Rates for the serial bonds with maturities:
o 2025 through 2030, 5.50 percent
o 2031 through 2035, 6.00 percent
From Johnson-Miller:
• The City Receives $3 million dollars
• The Interest Rates for the serial bonds with maturities:
o 2025 through 2027, 4.35 percent
o 2028 through 2032, 5.25 percent
o 2033 through 2035, 6.50 percent
From Shostak Corp:
• The City receives $2.9 million dollars
• The Interest rates for the serial bonds with maturities:
o 2025 to 2032, 5.75 percent
o 2033 to 2035, 6.25 percent
For each bid, compute the net interest cost (NIC) and the true interest cost (TIC). Which bid is more advantageous for the city?

Answer 1

Solution :

Note : the interest calculation here is pretty meticulous so for your understanding i have attached an excel formula sheet of all the 3 offers :

Net Interest Cost (NIC) : It is the notional interest cost that a bond issuer has to bear however it is not actual cost for issuer as this cost ignores time value of money which is taken care of in True interest cost(TIC).

Components of NIC calculation includes any discount, premium paid ( however this does not include time value of money)

***Formula NIC = (Total Interest Payments + Discount - Premium) / Number of Bond-Year Dollars***

True Interest Cost : It is similar to NIC but is more realistic in cost calculation since it includes time value of money and most widely used by bond issuers as it gives actual cost of interest

***Formula TIC = NIC / (1+ Discount rate)

1. Interest Paid calculation of Rogue Securities

A 1 Bond value 3000000 2 Rogue Sec. 3 No. of bond year dollars Maturity Interest Paid 4 Year Interest - $C$1*$D$9 0 5 44287 6 44652 -sc$1*$D$9 - SC$ 1 " $D$ 9 - $C$1*SD$9 7 45017 8 45383 0 0 c9*10 9 45748 100000 ( SC$ 1- C9 ) SD$9 0.055 E(Sc$1)- ( SC$9+$C$ 10))*$ D$9 10 46113 C10*9 100000 0.055 ($C$1)-(SC$9+$C$10+C11)) *$ D$9 11 46478 - C11 8 100000 0.055 ((SC$1)-(SC$9+$c$ 10+$ C$ 1 1+$ Cc$ 12) )*$ D$9 100000 =C12*7 0.055 12 46844 ={(SC$1)-(SC$9+SC$10+SC$11+$C$ 12+$C$13))*$ D$9 200000 13 47209 =C13* 6 0055 EC14*5 200000 =(SC$1)-(SC$9+$C$10+$C$11+$C$12+$C$ 13+$C$14))*SD$9 (SC$1 )- ( SC$9+$C$10+$C$ 11+$ C$12+$C$13+SC$14+SC$15))*$ D$9 14 47574 0.055 250000 o.06 15 47939 C15*4 =( SC$1 - ( SC$ 9+ $c$ 10+$C$ 1 1+$ C$ 12+$ C$ 13+$ C$ 14+$C$ 15+$ C$ 16))*$D$9 + $C$14+$C$ 15+$C$ 16+$C$ 17))*$D$9 14+SC$15+$C$16+$C$17+$C$18)) *$ D$9 - C16 * 3 C17*2 16 48305 250000 0.06 17 48670 18 49035 19 49400 250000 700000 0.06 E(($C$1)-( $C$9+$C$10+$C$11+$C$ (($C$1)- (SC$9+SC$10+$C$11+$C$ El(SC$1)-(SC$9+$C$ C18 1 0.06 C19 0 0.06 $17+$C$18+C19))*$D$9 750000 20 SUM(B9:B20) = ( SUM (E5: E20 )/S B$21 21 22 = 8550000 - 21.5175 % 23

NIC of Rogue Securities i.e marked green = 21.5175%

TIC ( since in question discount rate not given we assume it at 10% ), here no. of years = 15 i.e (2021-2035)
Thus, True interest cost = NIC / (1+0.1)^15 = 21.5175 / 0.239393 = 89.89 %

2.Interest Paid calculation of Jonson-miller :

G 1 Bond value 3000000 2 Jonson-miller 3 f bond vear dollars Maturity Year No Interest Rate Interest Paid 4 $C$1*SF$9 =sC$1*$F$9 - $C$1*SF$9 =$C$1*$F$9 5 44287 0 6 44652 O 7 45017 8 45383 C E((SC$1)-(SC$9))*$F$9 C9 10 o.0435 9 45748 100000 =($C$1}-(SC$9+$c$10))*SF$9 - C10 *9 0.0435 10 46113 100000 ((SC$1)-(SC$9+$c$10+$ C$ 1 1)) *SF$9 0.0435 11 46478 -C11 8 100000 11+$C$ 1 2 ) ) *$ F$9 lo.0525 = 100000 ( (SC$1)-(SC 12 46844 C12 * 7 2+$C$13))*$ F$9 0.0525 ( (SC$1 )- 13 47209 =C13 6 200000 C$13+$ C$ 14)) *$ F$9 $14+SC$15)) *SF$9 EC14* 5 0.0525 ={($C$1)-(SC$9 = ( ( $C$ 1 )- E ($C$1)-(SC$9+$C$10+$ CS E($C$1}(SC$9+$C$10+$C$11 ($C$1)-($C$9+$C$10+> E( ( Sc$1)- ( SC$9+$0 14 47574 200000 o.0525 250000 15 47939 =C15 4 0.0525 sc$14+SC$15+$C$16))*$ F$9 16 48305 =C16 3 250000 - C17 2 0.065 250000 sc$14+SC$15+sc$16+$C$ 17))*SF$9 17 48670 0.065 o.065 4+$C$15+$C$ 16+$C$17+$C$ 18))*SF$9 18 49035 C18*1 700000 C$17+SC$18+SC$19))* $F$9 19 49400 750000 -C19 0 20 (SUM(G5:G20))/$B$ 21 =17.0184 - SUM (B9: 820) 21 = 8550000 22 23

NIC of Jonson-miller i.e marked green = 17.0184%

TIC ( since in question discount rate not given we assume it at 10% ), here no. of years = 15 i.e (2021-2035)
Thus, True interest cost = NIC / (1+0.1)^15 = 17.0184 / 0.239393 = 71.09 %

3.Interest Paid calculation of Shostak-Corp :

2 Bond value 3000000 Shostak-Corp 4 Maturity Year No. of bond year dollars Interest Interest Paid sc$2*SH$10 6 44287 - -SC$2 $H$ 10 - $c$2*SH$10 - sC$2* SH$ 10 7 44652 8 45017 9 45383 lo.0575 Hl($C$2)-(SC$10))*SH$ 10 10 45748 -C10*10 100000 l(SC$2)-(SC$10+$C$11) )*S H$ 10 0.0575 C11*9 11 46113 100000 -[( SC$2 )- ($C$10+$c$11+$C$12))*$H$10 12 46478 -C12*8 100000 0.0575 ($C$2)-(SC$10+$C$11+$C$ 12+$c$13)) SH$ 10 13 46844 -C13#7 100000 0.0575 0.0575 ($C$2}{$C$10+$C$11+$C$12+$C$13+$C$14))*SH$10 -C14* 6 14 47209 200000 0.0575 = ( SC$2 ) - (S [( SCS2)- -C15* 5 200000 H$ 10 15 47574 =C16 4 ))*$H$10 16 47939 250000 00575 250000 17 48305 (SC SH$10 =C17 3 -c1812 18 2 ( (SC$2) - ( 18)) SH$10 18 48670 .02 - ( ( SC$2 ) - ( SC$3 19 49035 C19 1 18+SC$19)) $H$10 700000 0.0625 = ( ( SCS2) - ( SC$1 20 49400 - C20*0 0.0625 18+SC$19+SC$20))*SH$ 10 750000 21 ( SUM (16:121))/$B$22 =22.4956 % 22 -SUM(B10:B21) 8550000 23 24

NIC of Shostak-Corp i.e marked green = 22.4956%

TIC ( since in question discount rate not given we assume it at 10% ), here no. of years = 15 i.e (2021-2035)
Thus, True interest cost = NIC / (1+0.1)^15 = 22.4956 / 0.239393 = 93.96 %

Conclusion : Offer 1 is the best as it gives a high return to bond holders of 21.5% along with highest maturity value of $3.5 million