Based on response to 3 -8 Finance questionbelow, provide comments to the respons
ID: 2770541 • Letter: B
Question
Based on response to 3-8 Finance questionbelow, provide comments to the response.
3-8. The promised cash flows of three securities are listedhere. If the cash flows are risk free, and the risk-freeinterest rate is 5%, determine the no-arbitrage price of eachsecurity before the first cash flow is paid.
Security
Cash Flow Today ($)
Cash Flow in One Year ($)
A
500
500
B
0
1000
C
1000
0
Response:
Determine the non-arbitrage price of each security before thefirst cash flow is paid. Risk free interest rate is 5%.
Step 1. Put everything in terms of today’s dollars.Do that by dividing the cash flow ( in one year) by 1+ the riskfree interest rate (1.05, in this case).
Step 2. Equation 3.3 states that determine thenon-arbitrage price of a security: Price(Security) = PV(Allcash flows paid by the security). So you then addtoday’s CF to the PV of CF(in one year) to get the price ofthe security today.
Security
Cash Flow Today ($)
Cash Flow in One Year ($)
PV of CF in one year($)
NPV(or Price)
A
500
500
500 /1.05=476.19
500+476.19=976.19
B
0
1000
1000/1.05=952.38
0+952.38=952.38
C
1000
0
0/1.05=0
1000+0=1000
Security
Cash Flow Today ($)
Cash Flow in One Year ($)
A
500
500
B
0
1000
C
1000
0
Explanation / Answer
Present Value = Future Value / (1+r)t
Present Value of Security (or) Today’s Price of theSecurity = Present value of cash flows in one year (FV) / (1+riskfree interest rate)
Security A = $500 / 1.05 = 476.19 + $500
Security B = $1000 / 1.05 = 952.38 + $0
Security C = 0/1.05 = 0 = 0 +$1000
Here, Security A, B & C has Positive Net Present Values.These 3 Securities are in Strong arbitrage condition.
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