Suppose that I = 100, G = 75 and T = 100. There was a fall in autonomous level of consumption because of which the consumption function changed from C = 20 + 0.6YD to C’ = 10 + 0.6YD.

a) Calculate the equilibrium level of incomes associated with C and C’? Show your work. Does this change match up to what you calculated using the multiplier?

b) Calculate the equilibrium level of incomes associated with C and C’? But, this time use S + T = I + G condition. Show your work. Do you obtain the same conclusions as you did in part (a)?

c) What was C and what was S at the two equilibrium income levels?

d) Suppose the income associated with C was the full employment level of output and now you are at an output level associated with C’. By how much should G change to reach the full employment level? By how much should T change to reach the full employment level?

e) If the government wants to balance budget and at the same time reach the full employment level of output, what should it do?

You observe that the current three-year discount factor for default-risk free cash flows is 0.68. Remember, the t-year discount factor is the present value of $1 paid at time t, i.e. ???? = (1 + ????)−??, where ???? is the t-year spot interest rate (annual compounding). Assume all bonds have a face value of $100 and that all securities are default-risk free. All cash flows occur at the end of the year to which they relate. a) What is the price of a zero-coupon bond maturing in exactly 3 years? b) Your friend makes the following observation about the above bond: “Since there is no risk of default and there are no coupons to re-invest, buying the 3-year zero coupon bond today is a risk-free investment; that is, you are guaranteed to earn an annual return of 13.72% (i.e. 3-year spot rate)”. Explain why your friend is not entirely correct and how you would modify the statement to make it correct. c) In addition to the bond in (a), you observe the following: a 2-year coupon bond paying 10% annual coupons with a market price of $97, and two annuities that are trading at the same market price as each other. The first annuity matures in 3 years and pays annual cash flows of $20, while the second annuity pays annual cash flows of $28 and matures in 2 years. Using this information: i. Complete the term structure of interest rates, i.e. determine the one- and two-year discount factors, d1 and d2, respectively.

Helium at 200 kPa, 227 C is expanded in steady flow through a nozzle to 100 kPa. At these operating conditions the nozzle efficiency is 76%.

a) Making the usual nozzle assumptions, calculate the actual velocity at the nozzle exit. Start with the appropriate form of the first law.

b) Calculate the actual nozzle exit temperature.

An investor purchases a 10-year, 6% annual coupon payment bond at $90 per $100 of par value. The investor receives a series of 10 coupon payments of $6 (per 100 of par value) for a total of $60, plus the redemption of principal ($100) at maturity. In addition to collecting the coupon interest and the principal, the investor has the opportunity to reinvest the cash flows.

1) If the coupon payments are reinvested at 8%, per 100 of par value, what is the future value of the reinvested coupons at the end of the 10-year reinvestment period?

a) $79.085

b) $86.919

c) $82.899

29) Based on your answer from #28, and assuming you receive par back at maturity, the total return for this investment at the end of 10 years is:

a) $179.085

b) $186.919

c) $182.899

2) What would the realized rate of return (%) be on this investment?

a) 7.582%

b) 7.123%

c) 7.349%

3) What would the realized rate of return (%) be on this investment?

a) 7.582%

b) 7.123%

c) 7.349%

4) Let’s assume the investor in this security decided to sell the bond after 4 years. What would be the future value of reinvested coupons at this point again remembering that the investor is reinvesting the 6% coupons at an interest rate of 8%.

a) $26.248

b) $26.639

c) $27.037

5) If the investor sells the 10-year, 6% annual coupon bond after 4-years, assuming the coupons payments can be reinvested at 8% for its 10-year life, what would they realize in sale proceeds in year 4?

a) $90.754

b) $100.000

c) $95.234

6) The total return from the sale of the bond after 4-years is:

a) $127.037

b) $117.393

c) $117.791

7) In this example where the investor purchased the bond at $90 (discount price) and 4 years later sold the bond, the resulting gain or loss they incurred on the security is determined by comparing the sale price to the:

a) Original purchase price

b) Carrying Value

c) Original purchase price plus the amortized amount of the premium

8) An investor buys a 6% annual payment bond with 10 years to maturity. The bond has a YTM of 8% and is currently priced at $86.580 per 100 of par. What is the bond’s Macaulay Duration?

a) 7.2469 years

b) 7.8017 years

c) 7.6151 years

What will be the nominal rate of return on a perpetual preferred stock with a $100 par value, a stated dividend of 8% of par, and a current market price of (a) $56.00, (b) $77.00, (c) $104.00, and (d) $137.00? Round your answers to two decimal places.

1. %
   
2. %
   
3. %
   
4. %

XYZ limited had issued bonds with a par value of Rs. 100 and a coupon rate of 12% p.a. The bond has maturity of 30 months and pays quarterly coupons. Calculate the fair price of the bond if the required rate of return by investors is 8%.

A 10-year annual payment corporate bond has a market price of $1,050. It pays annual interest of $100 and its required rate of return is 9 percent. Is the bond fairly priced, underpriced, or overpriced? Also find the magnitude of the mispricing (if any).

A stock is currently trading at $100. Consider a European call option with 1 year to maturity
and strike price $105. The continuously compounded risk-free interest rate is 10% per annum.
The option currently trade at $7.5 Calculate the implied volatility.