# ABC is considering purchasing a smaller chain, XYZ software. ABC's financial analysts project...

## Question:

ABC is considering purchasing a smaller chain, XYZ software. ABC's financial analysts project that the merger will result in incremental net cash flows of $5.5 million in Year 1,$6.5 million in Year 2, $8.5 million in Year 3, and$15.5 million in year 4. Interest tax savings after the merger are estimated to be $1.8 million for each of the next 4 years. The expected cost of capital will be 10.5%, and the company expects to experience a normal growth of 6%, starting at the beginning of the fifth year. XYZ's outstanding debt is estimated to be$40 million, and the post-merger beta is estimated to be 1.50. The risk-free rate is 3.5%, and the market returns are 10%. What is the value of XYZ Software, to ABC software?

## Present value

Present value is a term used in time value of money which shows the time preference of money which means that money in future is less preferred over the money in present so future money should be compensated with some interest which makes it higher than the present value.

We first need to find the discount rate (K)

As per CAPM

K= risk free rate + market risk premium * beta = 3.5 +(10-3.5)*1.5=13.25%

Present value of first 4 cashflows =$5.5/1.1325 + 6.5/1.1325^2 + 8.5/1.1325^3 +15.5/1.1325^4=$25.20 m

PV of interest tax shields = E(1-(1+r)^-p)/r

Where

E= interest tax shields =$1.8m r= 13.25% P= 4 years Therefore PV =$1.8(1-1.1325^-4)/.1325=$5.33m Now the PV of terminal cashflows (at time 0) = F5/(K-g) * (1+K)^-4 Where g= growth rate =6% F5 = csshflow at time 5= F4(1+g)=$15.5(1.06)=$16.43 K= 13.25% Therefore PV =$16.43/(.1325-.06) * 1.1325^-4 =$137.77m Total value of XYZ software firm=$25.20+$1.8+$137.77=$164.77 Net value of XYZ software =$164.77 m -$40 m=$124.77 million 