The value of synergies is a critical output of any merger model This says that if we were to pay a premium for a company, let's say a premium of 2,000 Then the value of the synergies that you would earn from that company have to be greater than the 2,000 Thus we have to calculate the present value of synergies. Here we've got an example on the screen We start by taking the pre tax synergies and taxing them to find post tax And that's the cash flow the company will actually earn after the deal We then apply a discount rate of 10% to find the present value of those first three years of synergies And we also use the 10% to calculate a terminal value, including no growth Here the terminal value 2,100 has been calculated as the post tax synergies of 210 divided by the discount rate Thus the present value of the perpetuity We eventually get down to the value of synergies being 1,914.9 Great! So that is the absolute maximum premium that we should pay for a company If we paid 1,800, then that still leaves us with about 114.9 of value that we could earn However in this example, we're told that the total premium paid was 2,300, nightmare! It's the wrong way around, instead of creating value, we have destroyed it Some technical points to note along the way, where we're taxing our synergies We have assumed here that we're using the target's MTR (the marginal tax rate) So have we used the targets? Well fist of all we're going to assume that these are cost saving synergies And second of all, we're going to assume that those cost saving synergies are earned in the target company However, if that is not your assumptions and your synergies are going to be occurring in the acquirer Of course, use their marginal tax rate Secondly, when calculating a present value, you take cash flows and you discount them using the WACC However here we're going to add on a risk premium The reason for this is we are less certain of these synergy cash flows as to the normal cash flows that a company's been producing for a number of years In the terminal value, we've assumed no growth However you could assume low growth less than GDP growth rate Lastly the total premium paid to the target shareholders, if it's for a public company then that will be the acquisition equity value minus the pre offer market cap And that will give us the premium that we have paid above that pre offer market cap