A convertible security is an acknowledgment of debt (or preference share) which at a defined date may be converted into an ordinary share. The work begins by examining the characteristics of convertibles both overseas and in New Zealand. Chapter 2 suggests reasons for the rather late introduction of convertibles by New Zealand companies. A survey is made in Chapter 3 of 121 issues made from 1957 to 1975 by New Zealand companies and these are classified by year, type, interest rates and termination experience. An analysis is made of the use, and implications, of bonus issues of convertibles. The lack of options for the holder of convertibles issued by New Zealand companies coupled with the strong tendency for conversion to be at a fixed predetermined date renders valuation models developed overseas inapplicable to New Zealand. Alternative equations are developed in Chapter 4 and various uses for them are suggested. In Chapter 5 the model developed for New Zealand conditions is compared with others - principally with that of Brigham. A computer program was written to plot actual convergence patterns for issues which had matured by the end of 1975. It is demonstrated that convergence from below has been the general pattern as predicted by the valuation model - in contrast with the overseas experience of convergence from above. Discounts between share equivalent and convertibles are demonstrated to be substantial, generally to exceed predictive discounts and to persist well into the life cycle of the convertible. Chapter 6 builds upon the visual viewpoint of Chapter 5 by calculating ex post yields of, and yield differences between, shares and convertibles. A second computer program evaluates yields to pari passu dates from the time of the first listings of convertibles. Yield differences were also evaluated to and from alternative reference points - assuming later investment and earlier disinvestment. The general pattern emerging is for substantial yield differences in favour of convertibles and these tended to persist even if investment was made as late as two years, or even one year, prior to conversion dates. Chapter 7 extends the study by using the equations developed in Chapter 4 to evaluate issues still currently quoted and with maturities in 1977 or later. A third computer program was prepared to evaluate yields under various assumptions regarding taxation and dividend growth. The chapter is intended to demonstrate the feasibility of applying capital expenditure techniques incorporating sensitivity analysis for price changes as well as the tax and dividend variables to the problem of choice between shares or convertibles. Matrix presentations are developed to enable investment decisions to be made when the taxation impact upon interest and dividends differs. Finally, the 'switching decision' with associated transaction costs is incorporated into the analysis. A brief examination is undertaken of the problems associated with classification of convertibles in accounting reports and of the dilution or other effects of convertibles on various accounting ratio measurements. The study shows that ratio measures presented by New Zealand companies are rarely, if ever, made on a dual basis disclosing the dilutive or anti-dilutive effects. The work concludes with some suggestions for future research.