Nellie is evaluating two potential investments that she would buy today and sell

Question

Nellie is evaluating two potential investments that she would buy today and sell in 10 years. One is a bond and one is shares of stock . The 20 year bond has a face value of $100,000 and can be purchased to day for $90,000. It has 10 years until it matures. It pays semi-annual coupons with an annual rate of 3%. One hundred shares of the stock can be purchased today for $90,000. The company is forecasted to pay dividends of $500 quarterly for the 100 shares. The value of the stock in 10 years is expected to be $120,000. Which is the better investment based on the rate of return of each investment if they have equal risks? Nellie is evaluating two potential investments that she would buy today and sell in 10 years. One is a bond and one is shares of stock . The 20 year bond has a face value of $100,000 and can be purchased to day for $90,000. It has 10 years until it matures. It pays semi-annual coupons with an annual rate of 3%. One hundred shares of the stock can be purchased today for $90,000. The company is forecasted to pay dividends of $500 quarterly for the 100 shares. The value of the stock in 10 years is expected to be $120,000. Which is the better investment based on the rate of return of each investment if they have equal risks?

Explanation / Answer

The 20 year bond has a face value of $100,000 and can be purchased to day for $90,000. It has 10 years until it matures. It pays semi-annual coupons with an annual rate of 3%.

Semiannual bond. Coupon =3%. So PMT=3%*100000/2 = 1500

nper = 10*2= 20 period

Present value PV=90000

Maturity FV = 100,000

So Return on Bond = 2*Rate(nper,pmt,pv,fv)

= 2*Rate(20,1500,-90000,100000)

= 4.24% ...........(A)

One hundred shares of the stock can be purchased today for $90,000. The company is forecasted to pay dividends of $500 quarterly for the 100 shares. The value of the stock in 10 years is expected to be $120,000.

Which is the better investment based on the rate of return of each investment if they have equal risks?

Annual DIv = 4*500 = 2000

This will be paid for 10 Yrs.

ALso Capital gain in 10 Yrs = 120000-90000 = 30,000

We have FV=PV*(1+i)^n

So (1+i)^n = FV/PV = 120000/90000 = 1.3333

ie (1+i)^10 = 1.3333

So 1+i = (1.3333)^(1/10) =1.02918

SO i = 2.92%

DIv are qtrly. So FV of annuity of 500 for 10 yrs at 2.92%

= FVA of 500 for 10*4 = 40 periods at 2.92%/4

= 500*FVA(40,2.92%/4) = 500*46.2580 = 23129

So Total Return after 10 Yrs = 30000+23129 = 53129

So Avge return = (53129/90000)/10 = 5.90% ..(B)

So STock provides better return

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