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DCF Or CAGR On Frequent (SIP-Like) Investment

Hello,
I got the following question recently in an interview with an investment bank in UK. Need some help with the answer:

There are two scenarios for investment.

First case - I invest a fixed sum, say $1 million, in an index fund on 1Jan2001 as a lumpsum investment. Let’s say fund was priced at $100 per unit, so I receive 10,000 units on purchase date. I wait for 15 long years. On 31Dec2015, the fund was quoting at a price of $500 per unit, and I sell all 10,000 fund units. Net profit = 10,000 * ($500-$100) = 4 million.

Second case - I invest a fixed amount, say $66,666.67, on the first day of each year (like on 1Jan2001, 1Jan2002, 1Jan2003, …. upto 1Jan2015). In this case, each day’s fund price will be different so I’ll get different no. of units. After 15 years of such regular annual investment (from 1Jan01 to 1Jan15), I encash all my ‘X’ accumulated units of 31Dec2015 at the price of $500 per unit. Net profit will be X accumulated units * ($500-average buy price) = Whatever figure.

Question is - how do you compare the returns on the two investments?

My answer was CAGR was the right method for the first case, while DCF analysis was the right method for the second case. However, the intereviewer was not convinced and said that DCF needs risk-free rate (WACC) which changes every now and then. Additionally, he asked how CAGR and DCF results can be compared?

Can the experts help in providing some guidance?
1) What is the best method to compared the two scenarios?
2) If DCF, how to account for the changing risk-free rate? If CAGR, then how to account for each year’s investment in second scenario?

Thanks

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I’m not sure how usefeul wiil CAGR be in the 2nd case.

DCF can be used for both the cases but the assumption has to be made that the expected rate of return (WACC) remains same throughout. 

But if the interviewer says that the WACC keeps on changing then it will be cumbersome to account that in the DCF.

Hence, considering everything  in the scenario…

I think calculating an IRR will be the best method to compare both the cases. IRR won’t require any assumption of discounting factor and can be calculated for both the cases.