Question

[Please answer with details and explain why, I'm really confusing in these questions.]

1. General Electric issued $10 million worth of 20 year, 7% bonds in 2012. At the time, the required return was 6.25%. The current required return is 9.8%. If you purchased one of these bonds in 2012, how has the yield to maturity (YTM), current yield, and rate of return changed since 2012.

2. Microsoft and Google are both considering purchasing the small start up company, GigIT. Microsoft estimates that its IRR for buying GigIT is 11.5%. Google estimates its IRR for buying GigIT is 13.2%. Who makes the bid?

Answer 1

1. Let's assume that Face Value of these bonds is $ 1000 and the coupon payments are made annually.

In 2012,   Coupon Rate = 7% ; YTM = 6.25% ; n(No. of Coupon Payments) =20 ; Bond Price = P ; Coupon Payment, C = 1000 x 7% = 70

Using the YTM formula, P = C x (1 - (1+i)^-n / i + F / (1+i)ⁿ

=> P = 70 x (1 - (1+0.0625)^-20 / 0.0625 + 1000 / (1+0.0625)²⁰

=> P = 1084.31

You may use the PV formula in Excel to find the Bond Price

(If you want to take the assumption that coupon payments are made semi-annually, then you may take the rate as 0.0625/2 = 0.03125 and nper = 40 and Pmt = 35)

Current Yield = Coupon Payment per year / Current Bond Price = 70 / 1084.31 = 6.45%

In 2019,   Coupon Rate = 7% ; YTM = 9.8% ; n(No. of Coupon Payments) =13 (As it is 2019 now, 7 years have passed since the bond issue) ; Bond Price = P ; Coupon Payment, C = 1000 x 7% = 70

Using the YTM formula, P = C x (1 - (1+i)^-n / i + F / (1+i)ⁿ

=> P = 70 x (1 - (1+0.098)^-13 / 0.098 + 1000 / (1+0.098)¹³

=> P = 799

You may use the PV formula in Excel to find the Bond Price

Current Yield = Coupon Payment per year / Current Bond Price = 70 / 799 = 8.76%

Analysis

The Required rate of return, that is the YTM, which was 6.25% in 2012, has increased to 9.8% in 2019.

As we know that YTM and bond prices have an inverse relationship, consequently, the Bond prices have reduced from $1084.31 in 2012 to $799 in 2019. This inverse relationship is essentially because the investor wants to yield the YTM, so she will either shift to other bonds which offer returns equalling to YTM, or else will be willing to buy these bonds at a price where the return from bonds equal YTM, that is at lower bond prices.

The Current Yield has increased from 6.45% in 2012 to 8.76% in 2019, simply because as the bond prices reduce, the the coupon payments (which remain constant) as a percentage of Bond Prices will increase, because of their inverse relationship, as is evident from the Current Yield formula mentioned above.

2. IRR is the Internal Rate of Return. It measures the profitability of a business or a project. It is the discounting rate at which the Present value of Cash Inflows equals PV of Cash Outflows. Therefore, higher the IRR, more are the returns from the project/ business.

In reality, business decisions are not made using just a single metric, but if we consider only IRR as a factor to decide who makes the bid, we can say that the company for whom IRR is greater will make the bid. Hence, Google, whose estimated IRR @ 13.2% for buying GigIT is greater than that of Microsoft, will make the bid.

Google will make the bid.