Please help with YTM. Solution is in place, but cannot understand.

Please, help with understanding the following. Question: Titan Mining Corporation has 9 million shares of equity outstanding and 1,200,000 8.5 per cent semi-annual bonds outstanding, par value £100 each. The equity currently sells for £34 per share and has a beta of 1.20, and the bonds have 15 years to maturity and sell for 93 per cent of par. The market risk premium is 10 per cent, T-bills are yielding 5 per cent, and Titan Mining’s tax rate is 28 per cent. If Titan Mining is evaluating a new investment project that has the same risk as the firm’s typical project, what rate should the firm use to discount the project’s cash flows? Solution: Step 1. Find the cost of equality using the CAPM:

Re = 0.05 + 1.20(0.10) = 0.17 Step 2. The cost of debt is the YTM of the bonds. Therefore:

P0 = £93 = £4.25(PVIFAR%,30) + £100(PVIFR%,30)

R = 4.69% YTM = 4.69% × 2 = 9.38% Step 3. Find the after-tax cost of debt is:

Rd = (1 – .28)(.0938) = .0675 or 6.75% Step 4. Calculate the WACC:

WACC = .1700(.7328) + .0675 (.2672) = .1426 or 14.26%

Problem: I cannot understand Step 2. Where does £93 come from? Where does £4.25 come from? How did they calculate the entire equation with PVIFA? Please help and let me know if you have any questions!

The first to give a clear answer will be rewarded with 10 EUR ($11)!

Keep your EUR: I do this outta the goodness of my heart!

93 is the current market price of the outstanding bonds. The bond pays a semi-annual coupon of 8.5/2 = 4.25 and a face amount of 100 on the maturity date. All step 2 is doing is finding the bond equivalent yield of the remaining payments.

Sir, thank you! You do have a golden heart!

Now, I am trying to solve for PVIFA and PVIF but I have no idea how to do this. Is there some specific formula for those? How can I find them? I have spent 2 days over this problem. Is it time to call SOS?

Is there an alternative way to find YTM without using PVIFs?

I found these 2 calculators, giving the same answer of 0.0938:

This is the formula that does not rely on PVIFs:

I use the formula to get the number, but it still gives me 0.0929. What could I be doing wrong?

Use your financial calculator:

PV = -93; N=30; PMT = 4.25; FV=100; I/Y = ?? = 4.69

Since the 4.69 is the yield per six months, multiply by 2 to annualize it. x 2

Edited: I inadvertently put FV=1000 in the solution (Thanks, Mustafa, for catching it). I’ve corrected it so as not to cause confusion.

Use FV = 100 instead 1000