Question

The Energy Company wants to issue a new three-year bond with the following cash
flows:

Price (Today)	End Year	End Year	End Year
0	1	2	3
?	100	80	60

If there are no arbitrage opportunities, what is the price of this new bond?

Answer 1

Note : - The question ask to calculate price of bond and cash flows for 3 years are provided. But no rate of interest or coupon rate is provided in question, so i will solve this question taking 3 assumptions.

Formula for calculation of price of bond:-

Price of Bond (P₀) = CF₁/(1+r) + CF₂/(1+r)² + . . . . .+ CF_n/(1+r)ⁿ

where,

CF = Cash Flows of a year

r = Rate of Interest or Coupon rate of Bond

Assuming Rate of Interest is 6%,

Price of Bond = 100/(1+0.06) + 80/(1+0.06)² + 60/(1+0.06)³

= 94.3396 + 71.1997 + 50.3771

= 215.9165 (Rounded off)​​​​​​

Assuming Rate of Interest is 8%,

Price of Bond = 100/(1+0.08) + 80/(1+0.08)² + 60/(1+0.08)³

= 92.5926 + 68.5871 + 47.6299

= 208.8096 (Rounded off)​​​​​​

Assuming Rate of Interest is 10%,

Price of Bond = 100/(1+0.10) + 80/(1+0.10)² + 60/(1+0.10)³

= 90.9091 + 66.1157 + 45.0789

= 202.1037 (Rounded off)​​​​​​